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BEGIN:VEVENT
SUMMARY:Lecture/exercises 5
DTSTART;VALUE=DATE-TIME:20200731T140000Z
DTEND;VALUE=DATE-TIME:20200731T153000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-71@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Benjamin Peherstorfer (New York University)\nMultifi
delity and using data-fit models together with traditional model for\, e.g
.\, uncertainty quantification\n\nhttps://indico.mpi-magdeburg.mpg.de/even
t/7/contributions/71/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lecture/exercises 2
DTSTART;VALUE=DATE-TIME:20200728T120000Z
DTEND;VALUE=DATE-TIME:20200728T133000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-73@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Feliks Nüske (Paderborn University)\nStochastic Cal
culus\n- Stochastic Integral and SDEs\n- Ito’s Formula\n- The Generator
of an SDE\n- Examples\n\nhttps://indico.mpi-magdeburg.mpg.de/event/7/contr
ibutions/73/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lecture/exercises 4
DTSTART;VALUE=DATE-TIME:20200730T120000Z
DTEND;VALUE=DATE-TIME:20200730T133000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-75@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Feliks Nüske (Paderborn University)\nIntroduction t
o Kernel Methods for Data Driven Modeling\n- Kernel-based EDMD and Generat
or EDMD\n\nhttps://indico.mpi-magdeburg.mpg.de/event/7/contributions/75/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lecture/exercises 1
DTSTART;VALUE=DATE-TIME:20200727T160000Z
DTEND;VALUE=DATE-TIME:20200727T173000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-62@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: J. Nathan Kutz (University of Washington)\nIntroduct
ion to data-driven modeling\n- DMD\n- Koopman\n- Time-delay embeddings (HA
VOK)\n\nhttps://indico.mpi-magdeburg.mpg.de/event/7/contributions/62/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lecture/exercises 5
DTSTART;VALUE=DATE-TIME:20200731T120000Z
DTEND;VALUE=DATE-TIME:20200731T133000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-76@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Feliks Nüske (Paderborn University)\nCoarse Grainin
g for SDEs\n- Effective Dynamics\n- Reduced Generator\n- Parameter Estimat
ion\n\nhttps://indico.mpi-magdeburg.mpg.de/event/7/contributions/76/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lecture/exercises 2
DTSTART;VALUE=DATE-TIME:20200728T160000Z
DTEND;VALUE=DATE-TIME:20200728T173000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-63@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: J. Nathan Kutz (University of Washington)\nIntroduct
ion to DMD/Koopman for ROMs data-driven modeling\n- DMD integration into G
alerkin ROMs\n- Koopman/DMD models for ROMs\n\nhttps://indico.mpi-magdebur
g.mpg.de/event/7/contributions/63/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lecture/exercises 4
DTSTART;VALUE=DATE-TIME:20200730T160000Z
DTEND;VALUE=DATE-TIME:20200730T173000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-65@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: J. Nathan Kutz (University of Washington)\nIntroduct
ion to data-driven learning of physics models\n- The SINDy method\n- PDE-F
IND\n- ROMs with SINDy\n\nhttps://indico.mpi-magdeburg.mpg.de/event/7/cont
ributions/65/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lecture/exercises 5
DTSTART;VALUE=DATE-TIME:20200731T160000Z
DTEND;VALUE=DATE-TIME:20200731T173000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-66@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: J. Nathan Kutz (University of Washington)\nLearning
coordinates and models\n- SINDy autoencoders\n- Koopman autoencoders\n\nht
tps://indico.mpi-magdeburg.mpg.de/event/7/contributions/66/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lecture/exercises 1
DTSTART;VALUE=DATE-TIME:20200727T140000Z
DTEND;VALUE=DATE-TIME:20200727T153000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-67@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Benjamin Peherstorfer (New York University)\nIntrodu
ction to traditional (intrusive\, projection-based) model reduction\n- POD
/PCA\, greedy\n- Galerkin ROMs\n- DEIM\n\nhttps://indico.mpi-magdeburg.mpg
.de/event/7/contributions/67/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lecture/exercises 2
DTSTART;VALUE=DATE-TIME:20200728T140000Z
DTEND;VALUE=DATE-TIME:20200728T153000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-68@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Benjamin Peherstorfer (New York University)\n- Intru
sive ROMs: Error bounds: residual-based\; offline-online splitting\n- Reco
vering reduced models from data with operator inference (re-projection) an
d relation to DMD\n\nhttps://indico.mpi-magdeburg.mpg.de/event/7/contribut
ions/68/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lecture/exercises 3
DTSTART;VALUE=DATE-TIME:20200729T140000Z
DTEND;VALUE=DATE-TIME:20200729T153000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-69@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Benjamin Peherstorfer (New York University)\n- Opera
tor inference (non-Markovian terms for partial observations)\n- Probabilis
tic generalization bounds in limited situations for operator inference\n\n
https://indico.mpi-magdeburg.mpg.de/event/7/contributions/69/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Optimizing Intense Laser-Plasma Interactions with Evolutionary Alg
orithms and Machine Learning
DTSTART;VALUE=DATE-TIME:20200727T173000Z
DTEND;VALUE=DATE-TIME:20200727T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-145@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Joseph Smith (The Ohio State University)\nIntense la
sers have the ability to accelerate ions to high energies over very short
distances\, but the beam quality generated through these methods is not ye
t ready for many applications. We developed a framework using evolutionary
algorithms to automatically run thousands of one-dimensional (1D) particl
e-in-cell simulations to optimize the conversion from laser energy to ion
energy. The “optimal” 1D target found with this approach also outperfo
rmed conventional targets in more-realistic fully-three-dimensional (3D) s
imulations. We plan to extend this approach to develop synthetic datasets
and use machine learning techniques to help control ion beam properties an
d to better understand the complex relationship between computationally-in
expensive reduced-dimensionality (1D/2D) simulations with more realistic\,
but computationally-expensive 3D simulations and experiments.\n\nhttps://
indico.mpi-magdeburg.mpg.de/event/7/contributions/145/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/145/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Deep learning based model reduction approaches in flow models
DTSTART;VALUE=DATE-TIME:20200730T110000Z
DTEND;VALUE=DATE-TIME:20200730T120000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-188@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Yiran Wang (The Chinese University of Hong Kong)\nIn
this paper\, we intend to use a deep-learning based approach for the cons
truction of locally conservative flux fields with heterogeneous and high-c
ontrast media in the context of flow models. In previous work\, the proble
m is solved through a variation of the Generalized Multiscale Finite Eleme
nt Method(GMsFEM)\, which is computationally expensive. The key ingredient
s of GMsFEM include multiscale basis functions and coarse-scale parameters
\, which are obtained by solving local problems in each coarse neighborhoo
d. In case of the time-dependent media\, we have to recompute key ingredie
nts in different time steps. The objective of our work is to make use of d
eep learning techniques to mimic the nonlinear relation between the permea
bility field and the GMsFEM discretizations\, and use neural networks to p
erform fast computation of GMsFEM ingredients repeatedly for a class of me
dia. The flux values are obtained through the use of a Ritz formulation in
which we argument the resulting linear system of the continuous Garlerkin
(CG) formulation in the higher-order GMsFEM approximation space. Furthermo
re\, we postprocess the velocity field with some postprocessing approaches
to obtain the local conservation property.\n\nhttps://indico.mpi-magdeburg
.mpg.de/event/7/contributions/188/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/188/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive
Physics Informed Neural Networks
DTSTART;VALUE=DATE-TIME:20200727T173000Z
DTEND;VALUE=DATE-TIME:20200727T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-149@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Colby Wight (PNNL)\nPhase field models\, in particul
ar\, the Allen-Cahn type and Cahn-Hilliard type equations\, have been wide
ly used to investigate interfacial dynamic problems. Designing accurate\,
efficient\, and stable numerical algorithms for solving the phase field mo
dels has been an active field for decades. We focus on using the deep neur
al network to design an automatic numerical solver for the Allen-Cahn and
Cahn-Hilliard equations by proposing an improved physics informed neural n
etwork (PINN). Though the PINN has been embraced to investigate many diffe
rential equation problems\, we find a direct application of the PINN in so
lving phase-field equations won't provide accurate solutions. Thus\, we pr
opose various techniques that add to the approximation power of the PINN.
As a major contribution of this paper\, we propose to embrace the adaptive
idea in both space and time and introduce various sampling strategies\, s
uch that we are able to improve the efficiency and accuracy of the PINN on
solving phase field equations. In addition\, the improved PINN has no res
triction on the explicit form of the PDEs\, making it applicable to a wide
r class of PDE problems and sheds light on numerical approximations of oth
er PDEs in general. simulations.\n\nhttps://indico.mpi-magdeburg.mpg.de/ev
ent/7/contributions/149/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/149/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The use of machine learning in Computational Fluid Dynamics for an
economic approach to flow optimization problems.
DTSTART;VALUE=DATE-TIME:20200730T110000Z
DTEND;VALUE=DATE-TIME:20200730T120000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-147@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Georg Schatzdorfer (TU Graz)\nAs in many engineering
fields\, Computational Fluid Dynamics (CFD) lives upon modelling reality
in a feasible way to come to a desired solution. One good example in flui
d dynamics is turbulence\, which is mathematical modelled in most simulati
ons\, but there are many cases where it is necessary to resolve turbulent
eddy’s to take crucial effects into consideration. If this is coupled wi
th a flow optimization problem\, the computation time becomes a limiting f
actor for companies. An example were machine learning solves a CFD problem
like this is in multiphase flow simulation [1]. Where a computationally i
ntensive problem is solved with less processing time. \nBuild on the resea
rch of *Peter A. Leitl* Et al. [2] where the flow in the turbine centre fr
ame (TCF)\, which is the part between high and low pressure turbine in an
aircraft engine\, was improved\, we will investigate optimization methods
for the first stage low pressure turbine in consideration of the changed f
low field due to the application of drag reducing micro channel surfaces i
n the TCF.\n\n[1] Ansari\, A.\, Boosari\, S. S. H.\, & Mohaghegh\, S. D. (
2020). *Successful Implementation of Artificial Intelligence and Machine L
earning in Multiphase Flow Smart Proxy Modeling: Two Case Studies of Gas-L
iquid and Gas-Solid CFD Models*. J Pet Environ Biotechnol\, 11\, 401.\n[2]
Leitl\, P. A.\, Göttlich\, E.\, Flanschger\, A.\, Peters\, A.\, Feichtin
ger\, C.\, Marn\, A.\, & Reschenhorfer\, B. (2020). *Numerical investigati
on of optimal riblet size for turbine center frame strut flow and the impa
ct on the performance*. AIAA Scitech 2020 Forum\, 307.\n\nhttps://indico.m
pi-magdeburg.mpg.de/event/7/contributions/147/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/147/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Learning Constitutive Relations using Symmetric Positive Definite
Neural Networks
DTSTART;VALUE=DATE-TIME:20200727T173000Z
DTEND;VALUE=DATE-TIME:20200727T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-156@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Kailai Xu (Stanford University)\nWe present a new ne
ural-network architecture\, called the Cholesky-factored symmetric positiv
e definite neural network (SPD-NN)\, for modeling constitutive relations i
n computational mechanics. Instead of directly predicting the stress of th
e material\, the SPD-NN trains a neural network to predict the Cholesky fa
ctor of the tangent stiffness matrix\, based on which the stress is calcul
ated in the incremental form. As a result of this special structure\, SPD-
NN weakly imposes convexity on the strain energy function\, satisfies time
consistency for path-dependent materials\, and therefore improves numeric
al stability\, especially when the SPD-NN is used in finite element simula
tions. Depending on the types of available data\, we propose two training
methods\, namely direct training for strain and stress pairs and indirect
training for loads and displacement pairs. We demonstrate the effectivenes
s of SPD-NN on hyperelastic\, elasto-plastic\, and multiscale fiber-reinfo
rced plate problems from solid mechanics. The generality and robustness of
SPD-NN make it a promising tool for a wide range of constitutive modeling
applications.\n\nhttps://indico.mpi-magdeburg.mpg.de/event/7/contribution
s/156/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/156/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nonlinear model reduction for one-dimensional solidification proce
ss in additive manufacturing
DTSTART;VALUE=DATE-TIME:20200727T173000Z
DTEND;VALUE=DATE-TIME:20200727T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-221@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Parisa Khodabakhshi (Oden Institute for Computationa
l Engineering and Sciences\, UT Austin)\nDue to the notable potentials of
additive manufacturing (AM)\, the interest in AM has risen significantly a
cross several industries during the past decade. One of the key factors go
verning the mechanical properties of an additively-manufactured part is th
e solidification microstructure. However\, the spatial and temporal resolu
tion required for the simulation of the solidification process is several
orders of magnitude smaller than the dimensions of the final part imposing
infeasibly high computational expenses on the simulations. Model order re
duction can potentially help reduce this computational burden and allow fo
r the development of microstructure-aware models at part scale. We have de
veloped a projection-based model reduction for a one-dimensional solidific
ation model consisting of the phase-field equation for the order parameter
coupled with the heat equation. The inherent nonlinearity of the full mo
del is accounted for by lifting transformations to expose a polynomial str
ucture where the operators of the ROM for the lifted model are learned non
-intrusively using the operator inference method (OpInf). Owing to the non
-intrusive nature of OpInf\, the lifted form need not be discretized and s
olved\, and its ROM operators are learned from snapshots of the original f
ull model.\n\nhttps://indico.mpi-magdeburg.mpg.de/event/7/contributions/22
1/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/221/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wavelet based dynamic mode decomposition
DTSTART;VALUE=DATE-TIME:20200729T173000Z
DTEND;VALUE=DATE-TIME:20200729T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-159@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Manu Krishnan (PhD Candidate\, Department of Aerospa
ce and Ocean Engineering\, Virginia Tech)\nDynamic Mode Decomposition (DMD
) has emerged as a prominent data-driven technique to identify the spatio-
temporal coherent structures in dynamical systems\, owing to its strong re
lation with the Koopman operator. For dynamical systems with inputs (exter
nal forcing) and outputs (measurement)\, the input-output DMD (ioDMD) prov
ides a natural extension to DMD so that the learned model approximates the
input-output behavior of the underlying dynamics. Both DMD and ioDMD assu
me access to full-state measurements. In this work\, we propose a novel
methodology\, called the wavelet-based DMD (WDMD)\, that integrates wavel
et decompositions with ioDMD to approximate dynamical systems from partial
measurement data. Our non-intrusive approach constructs numerical models
directly from trajectories of the inputs and outputs of the full model\, w
ithout requiring the full-model operators. These trajectories are generate
d by running a simulation of the full model or by observing the response o
f the original dynamical systems to inputs in an experimental framework.
The performance of WDMD is explained through the use of modeling the inp
ut output vibrational response of a hollow cantilever beam. We illustrate
the effectiveness of WDMD using both simulated beam data and experimental
measurements.\n\nhttps://indico.mpi-magdeburg.mpg.de/event/7/contributions
/159/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/159/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adaptive Interpolatory MOR by Learning the Error Estimator in the
Parameter Domain
DTSTART;VALUE=DATE-TIME:20200729T173000Z
DTEND;VALUE=DATE-TIME:20200729T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-151@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Sridhar Chellappa (Max Planck Institute for Dynamics
of Complex Technical Systems)\nInterpolatory methods offer a powerful fra
mework for generating reduced‑order models for non‑parametric or param
etric systems with time‑varying inputs. Choosing the interpolation point
s adaptively remains an area of active interest. A greedy framework has be
en introduced in [1\, 2] to choose interpolation points automatically usin
g a posteriori error estimators. Nevertheless\, when the parameter range i
s large or if the parameter space dimension is larger than two\, the greed
y algorithm may take considerable time\, since the training set needs to i
nclude a considerable number of parameters.\n\nIn this work\, we introduce
an adaptive training technique by learning an efficient a posteriori erro
r estimator over the parameter domain. A fast learning process is created
by interpolating the error estimator using radial basis functions over a f
ine parameter training set\, representing the whole parameter domain. The
error estimator is evaluated only on a coarse training set consisting of o
nly a few parameter samples. The algorithm is an extension of the work in
[3] to interpolatory model order reduction in the frequency domain. Possib
ilities exist to use other sophisticated machine‑learning techniques lik
e artificial neural networks\, etc. to learn the error estimator\, based o
n data at a few parameter samples. However\, we do not pursue this in the
present work. Selected numerical examples demonstrate the efficiency of th
e proposed approach.\n\n**References**\n\n[1] Feng\, L.\, Antoulas\, A.C.\
, Benner\, P.: Some a posteriori error bounds for reduced‑order modellin
g of (non‑)parametrized linear systems. ESAIM: Math. Model. Numer. Anal.
51(6)\, 2127–2158 (2017).\n\n[2] Feng\, L.\, Benner\, P.: A new error e
stimator for reduced‑order modeling of linear parametric systems. IEEE T
rans. Microw. Theory Techn. 67(12)\, 4848–4859 (2019).\n\n[3] Chellappa\
, S.\, Feng\, L.\, Benner\, P.: An adaptive sampling approach for the redu
ced basis method. e‑prints 1910.00298\, arXiv (2019). URL https://arxiv.
org/abs/1910.00298. Math.NA.\n\n[4] Chellappa\, S.\, Feng\, L.\, de la Rub
ia\, V.\, Benner\, P.: Adaptive Interpolatory MOR by Learning the Error Es
timator in the Parameter Domain. e‑prints 2003.02569\, arXiv (2020). \nU
RL https://arxiv.org/abs/2003.02569. Math.NA.\n\nhttps://indico.mpi-magdeb
urg.mpg.de/event/7/contributions/151/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/151/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Analysis of bubble dynamics using data-driven dynamical systems an
d machine learning
DTSTART;VALUE=DATE-TIME:20200727T173000Z
DTEND;VALUE=DATE-TIME:20200727T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-150@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Andrew J. Gibson (Department of Mechanical and Aeros
pace Engineering\, University of Colorado Colorado Springs)\nThe formation
and oscillation of bubbles is important in cavitation related to turbomac
hinery\, and in biomedical applications\, such as contrast-enhanced ultras
ound imaging and drug delivery for cancer treatment. There is an extensive
literature on the modeling and analysis of bubble oscillations in these s
ettings\, allowing for detailed simulations from first principles. However
\, there are still many open questions that may benefit from machine learn
ing (ML). In this research\, we apply data-driven and ML methods to analyz
ing and controlling the nonlinear dynamics of bubble oscillations. In this
context\, the Rayleigh-Plesset equation (RPE) is a central object of stud
y [1]. It exhibits richly-structured chaotic solutions when describing an
acoustically-driven bubble for certain parameter values [2]. Nonspherical
shape modes - which are important for enhancing ultrasound imaging and pro
moting drug delivery - can be overlaid as perturbations to the basic spher
ical mode [3\, 4\, 5]\, leading to a dynamical system of much higher dimen
sion. Recently\, experimental studies of bubble shape modes evolving in ac
oustic fields have captured large amounts of high-quality time series data
[6\, 7\, 8\, 9]. We are therefore interested in discovering reduced-order
models of microbubble dynamics from raw experimental data and comparing t
hese to data-driven analyses of first-principle\, physics-based models. Ad
ditionally\, we want to apply our data-driven model to develop a framework
for nonlinear control [10] of both individual bubbles and bubbly flows us
ing acoustic forcing. To this end\, we have developed a deep neural networ
k (DNN) to forecast time series previously generated numerically from the
RPE. We intend to train this on experimental time series and use it to pre
dict the dynamic response of bubbles to changes in acoustic forcing. We ar
e also exploring the Singular Value Decomposition (SVD) of Hankel matrices
built from these time series to identify a Koopman embedding of the RPE w
hen acoustically-driven. This Koopman embedding provides a coordinate syst
em wherein the nonlinear dynamics of bubble oscillations becomes linear\,
allowing the application of tools from classical control theory.\n\nRefere
nces\n[1] Christopher Earls Brennen. Cavitation and Bubble Dynamics. Cambr
idge University Press\, Cambridge\, 2013.\n[2] Werner Lauterborn and Engel
bert Suchla. Bifurcation Superstructure in a Model of Acoustic Turbulence.
Physical Review Letters\, 53(24):2304-2307\, December 1984. Publisher: Am
erican Physical Society.\n[3] Michael Calvisi\, Olgert Lindau\, John Blake
\, and Andrew Szeri. Shape Stability and Violent Collapse of Microbubbles
in Acoustic Traveling Waves. Physics of Fluids\, 19\, April 2007.\n[4] M.
S. Plesset. On the Stability of Fluid Flows with Spherical Symmetry. Journ
al of Applied Physics\, 25(1):96-98\, January 1954. Publisher: American In
stitute of Physics.\n[5] Matthieu Guedra and Claude Inserra. Bubble shape
oscillations of finite amplitude. Journal of Fluid Mechanics\, 857:681-703
\, 2018. Edition: 2018/10/25 Publisher: Cambridge University Press.\n[6] S
arah Cleve\, Matthieu Guedra\, Claude Inserra\, Cyril Mauger\, and Philipp
e Blanc-Benon. Surface modes with controlled axisymmetry triggered by bubb
le coalescence in a high-amplitude acoustic field. Physical Review E\, 98\
, September 2018.\n[7] M. Guedra\, C. Inserra\, B. Gilles\, and C. Mauger.
Periodic onset of bubble shape instabilities and their influence on the s
pherical mode. In 2016 IEEE International Ultrasonics Symposium (IUS)\, pa
ges 1-4\, September 2016. Journal Abbreviation: 2016 IEEE International Ul
trasonics Symposium (IUS).\n[8] Matthieu Guedra\, Sarah Cleve\, Cyril Maug
er\, Philippe Blanc-Benon\, and Claude Inserra. Dynamics of nonspherical m
icrobubble oscillations above instability threshold. Physical Review E\, 9
6(6):063104\, December 2017. Publisher: American Physical Society.\n[9] Ma
tthieu Guedra\, Sarah Cleve\, Cyril Mauger\, Claude Inserra\, and Philippe
Blanc-Benon. Time-resolved dynamics of micrometer-sized bubbles undergoin
g shape oscillations. The Journal of the Acoustical Society of America\, 1
41:3736-3736\, May 2017.\n[10] Joshua Proctor\, Steven Brunton\, and J. Ku
tz. Generalizing Koopman Theory to Allow for Inputs and Control. SIAM Jour
nal on Applied Dynamical Systems\, 17\, February 2016.\n\nhttps://indico.m
pi-magdeburg.mpg.de/event/7/contributions/150/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/150/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Analyzing the Transition to Buffeting of a 2D Airfoil using the Dy
namic Mode Decomposition
DTSTART;VALUE=DATE-TIME:20200727T173000Z
DTEND;VALUE=DATE-TIME:20200727T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-177@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Sathsara Dias (Clarkson University)\nThe Dynamic Mod
e Decomposition (DMD) algorithm was first introduced in the fluid mechanic
s community for analyzing the behavior of nonlinear systems. DMD processes
empirical data and produces approximations of eigenvalues and eigenvector
s (“DMD modes”) of the linear Koopman operator that represents the non
linear dynamics. In fluid dynamics\, this approach has been used to both a
nalyze constituent flow patterns in complex flows\, and to design control
and sensing strategies. In this work\, we focus on predicting the transiti
on to buffeting of a 2D airfoil in a transonic regime. Buffeting is a vibr
ation that occurs as the angle-of-attack increases and the interactions be
tween the shock and flow separation induce limit-cycle oscillations. We de
monstrate that this bifurcation can be predicted by tracking the eigenvalu
e with the greatest real part across a range of parameter values $\\alpha$
\, which is the airfoil's angle. We evaluate the performance of our approa
ch on a synthetic Hopf-bifurcation flow and both pseudo-time simulations o
f a standard 2D airfoil. As part of the next stage of this research analys
is for the time-resolved simulations of a standard 2D airfoil is carried o
ut.\n\nhttps://indico.mpi-magdeburg.mpg.de/event/7/contributions/177/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/177/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Deep learning of superstructures in turbulence
DTSTART;VALUE=DATE-TIME:20200730T110000Z
DTEND;VALUE=DATE-TIME:20200730T120000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-222@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Manuel Schaller (TU Ilmenau)\, Friedrich Philipp (TU
Ilmenau)\, Mitsuru Wilson (TU Ilmenau)\nWe aim to utilize machine learnin
g methods to learn superstructures in turbulent flow to obtain a data-driv
en reduced model for turbulent convection. The underlying data will stem f
rom both numerical simulations and experiments and will be used as trainin
g data for various machine learning architectures in order to predict the
behavior of the underlying system and to extract hidden structures of the
turbulent flow.\n\nhttps://indico.mpi-magdeburg.mpg.de/event/7/contributio
ns/222/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/222/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The Construction and Application of Surrogate Models for Sensitivi
ty Analysis
DTSTART;VALUE=DATE-TIME:20200730T110000Z
DTEND;VALUE=DATE-TIME:20200730T120000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-155@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Xifu Sun (Australian National University)\nIn the fi
eld of environmental modelling\, especially modelling problems in the wate
r resources sector\, the acquisition of observation data is usually expens
ive\, and/or the underlying model representations are incredibly complex.
The spatially distributed models typically used for water quantity and qua
lity prediction yield significant uncertainties even after being carefully
calibrated\, and they tend to have a high computational cost with long ru
ntimes. These issues profoundly affect the performance of the models and i
mpact the efficiencies of sensitivity and uncertainty analysis\; ultimatel
y\, achieving robust decision making is very difficult for end-users who n
eed knowledge of the behaviour of such models and the credibility of their
predictions.\nMachine learning can provide a means for the practical cons
truction of surrogate models of the original response surface by learning
from data\, and this dramatically helps with computational efficiency and
performance. Currently\, several machine learning techniques such as Gauss
ian processes and polynomial chaos expansions have been widely used for ge
nerating surrogate models\, but a gap still exists on how to efficiently c
ombine the surrogate model construction and sensitivity analysis.\nSensiti
vity analysis relies heavily on the sampling choices and model runtimes. H
ow can different sampling methods be designed to more efficiently explore
the behaviour of surrogate models\, and how to best construct surrogate mo
dels to assist the convergence of sensitivity analysis metrics? These are
still challenging problems. Machine learning techniques will be explored a
s a potential solution to these challenging problems.\n\nKeywords: Machine
Learning\; Environmental Modelling\; Hydrological Modelling\; Sensitivity
Analysis\; Surrogate Model\; Uncertainty\n\nhttps://indico.mpi-magdeburg.
mpg.de/event/7/contributions/155/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/155/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Data-based soil-tool interaction force prediction based on measure
ments and the Discrete Element Method
DTSTART;VALUE=DATE-TIME:20200730T110000Z
DTEND;VALUE=DATE-TIME:20200730T120000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-235@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Jonathan Jahnke (Fraunhofer ITWM)\nWe are interested
in real-time capable simulation of soil and soil-tool interaction forces.
In previous work\, we have successfully implemented a solution of precomp
uting data using the Discrete Element Method (DEM) and efficiently process
ing and saving it in a lookup table. Within the respective online phase\,
the data is accessed in an efficient way [1\,2]. \nWe also perform measure
ments at a test pit at the soil laboratory at TUK with different kinds of
soil\, e.g. coarse gravel and coarse sand. We plan to use this data to in
clude the frequency behavior in the reaction forces in order to improve th
e above mentioned approach. Interesting signal processing tools which may
be used here comprise Fourier Transform\, Power Spectral Density and other
s. \n\n[1] Jahnke\, J.\; Steidel\, S.\; Burger\, M. Soil Modeling with a D
EM Lookup approach\, PAMM\, 2019\n[2] Jahnke\, J.\; Steidel\, S.\; Burger\
, M.\; Simeon\, B. Efficient Particle Simulation Using a Two-Phase DEM-Loo
kup Approach\, Proceedings of the 9th ECCOMAS on MBD\, pp. 425-432\, 2020\
n\nhttps://indico.mpi-magdeburg.mpg.de/event/7/contributions/235/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/235/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Machine Learning Algorithms for Learning Nonlinear Terms of Reduce
d Mechanical Models in Explicit Structural Dynamics
DTSTART;VALUE=DATE-TIME:20200730T110000Z
DTEND;VALUE=DATE-TIME:20200730T120000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-199@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Jonas Kneifl (Institute of Engineering and Computati
onal Mechanics)\nModeling and simulations are a pillar in the development
of complex technical systems. However\, for time-critical applications a c
onduction of high-fidelity simulations is not always feasible. To mitigate
this computational bottleneck model order reduction (MOR) can be applied.
For nonlinear models\, linear MOR approaches are only practicable to a li
mited extend. Nonlinear approaches\, on the contrary\, often require deep
interventions in the used simulation code. If access is not possible\, non
-intrusive nonlinear model order reduction can be the key to success.\nThe
goal of this work is to implement two different non-intrusive approaches
using linear model order reduction along with machine learning algorithms.
They both rely on the idea to learn the dynamics in the reduced space. In
the first approach\, a linear ODE is supplemented with the nonlinear inne
r forces discovered by the algorithms. In contrast\, the second one aims t
o learn the sequence of the reduced dynamics of a system directly.\nBy app
lying these methods to problems arising from the field of structural dynam
ics\, accurate surrogate models are received. They can speed up the simula
tion time significantly\, while still providing high-quality state approxi
mations.\n\nhttps://indico.mpi-magdeburg.mpg.de/event/7/contributions/199/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/199/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sensor selection for hyper-parameterized linear Bayesian inverse p
roblems
DTSTART;VALUE=DATE-TIME:20200729T173000Z
DTEND;VALUE=DATE-TIME:20200729T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-153@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Nicole Aretz-Nellesen (RWTH Aachen)\nMathematical mo
dels of physical processes often depend on parameters\, such as material p
roperties or source terms\, that are known only with some uncertainty. Mea
surement data can help estimate these parameters and thereby improve the m
eaningfulness of the model. As experiments can be costly\, it is important
to choose sensor positions carefully to obtain informative data on the un
known parameter. In this poster we consider an observability coefficient t
hat characterizes the sensitivity of measurements to parameter changes\, a
nd show its connection to optimal experimental design criteria. We then sh
ow how the observability coefficient can be used for sensor selection.\n\n
https://indico.mpi-magdeburg.mpg.de/event/7/contributions/153/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/153/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Data-Driven Identification and Reduction of Dynamical Systems with
the Loewner Framework
DTSTART;VALUE=DATE-TIME:20200729T173000Z
DTEND;VALUE=DATE-TIME:20200729T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-158@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Dimitrios S. Karachalios (MPI-DRI)\nIdentifying dyna
mical systems from measured data is an important step towards accurate mod
eling and control. Model order reduction (MOR) constitutes a class of meth
ods that can be used to replace large\, complex models of dynamical proces
ses with simpler\, smaller models. The reduced-order models (ROMs) can be
then used for further tasks such as control\, design\, and simulation. One
typical approach for projection-based model reduction for both linear and
non-linear dynamical systems is by employing interpolation. Projection-ba
sed methods require access to the internal dynamics of the system which is
not always available. The aim here is to compute ROMs without having acce
ss to the internal dynamics\, by means of a realization-independent method
. The proposed methodology will fall into the broad category of data-drive
n approaches.\n\nThe method under consideration\, which will be referred t
o as the Loewner framework (LF)\, was originally introduced by the third a
uthor. Based on data\, LF identifies state-space models in a direct way. I
n the original setup\, the framework relies on compressing the full data s
et to extract dominant features and\, at the same time\, to eliminate the
inherent redundancies. In the broader class of nonlinear control systems\,
the LF has been already extended to certain classes with a special struct
ure such as quadratic or bilinear systems. As an application of the aforem
entioned method is the well studied Lorenz attractor in comparison with ot
her model learning techniques.\n\nhttps://indico.mpi-magdeburg.mpg.de/even
t/7/contributions/158/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/158/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Artificial neural network for bifurcating phenomena modelled by no
nlinear parametrized PDEs
DTSTART;VALUE=DATE-TIME:20200729T173000Z
DTEND;VALUE=DATE-TIME:20200729T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-181@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Federico Pichi (SISSA\, International School for Adv
anced Studies)\n**Artificial neural network for bifurcating phenomena mode
lled by nonlinear parametrized PDEs**\n\n\nThe aim of this work is to show
the applicability of the Reduced Basis (RB) model reduction and Artificia
l Neural Network (ANN) dealing with parametrized Partial Differential Equa
tions (PDEs) in nonlinear systems undergoing bifurcations.\n\nBifurcation
analysis\, i.e.\, following the different bifurcating branches due to the
non-uniqueness of the solution\, as well as determining the bifurcation po
ints themselves\, are complex computational tasks. Reduced Order Models (R
OM) and Machine Learning (ML) techniques can potentially reduce the comput
ational burden by several orders of magnitude.\n\nModels describing bifurc
ating phenomena arising in several fields with interesting applications\,
from continuum to quantum mechanics passing through fluid dynamics [4\,5\,
6].\n\nFollowing the approach in [1\, 2]\, we analyzed different bifurcati
ng test cases where both physical and geometrical parameters were consider
ed. In particular\, we studied the Navier-Stokes equations for a viscous\,
steady and incompressible flow in a planar straight channel with a narrow
inlet.\nWe reconstructed the branching solutions and explored a new empir
ical strategy in order to employ the RB and ANN for an efficient detection
of the critical points.\n\nAll the simulations were performed within the
open source software FEniCS and RBniCS [7] for the ROM\, while we chose Py
Torch to construct the neural network.\n\n**References**\n\n[1] M. Guo and
J. S. Hesthaven. Data-driven reduced order modeling for time-dependent pr
oblems. Computer methods in applied mechanics and engineering\, 345:75–9
9\, 2019.\n\n[2] J. S. Hesthaven and S. Ubbiali. Non-intrusive reduced ord
er modeling of nonlinear problems using neural networks. Journal of Comput
ational Physics\, 363:55–78\, 2018.\n\n[3] F. Pichi\, F. Ballarin\, J. S
. Hesthaven\, and G. Rozza. Artificial neural network for bifurcating phe-
nomena modelled by nonlinear parametrized PDEs. In preparation\, 2020.\n\
n[4] F. Pichi\, A. Quaini\, and G. Rozza. A reduced order technique to stu
dy bifurcating phenomena: application to the Gross-Pitaevskii equation. Ar
Xiv preprint https://arxiv.org/abs/1912.06089\, 2019.\n\n[5] F. Pichi and
G. Rozza. Reduced basis approaches for parametrized bifurcation problems h
eld by non-linear Von Kármán equations. Journal of Scientific Computing\
, 339:667–672\, 2019.\n\n[6] M. Pintore\, F. Pichi\, M. Hess\, G. Rozza\
, and C. Canuto. Efficient computation of bifurcation diagrams with a defl
ated approach to reduced basis spectral element method. ArXiv preprint arX
iv:1907.07082\, 2019.\n\n[7] RBniCS. http://mathlab.sissa.it/rbnics.\n\nht
tps://indico.mpi-magdeburg.mpg.de/event/7/contributions/181/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/181/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Discovering the governing PDE of an active nematic system from vid
eo data
DTSTART;VALUE=DATE-TIME:20200727T173000Z
DTEND;VALUE=DATE-TIME:20200727T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-165@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Connor Robertson (New Jersey Institute of Technology
)\nWithin each animal cell is a complex infrastructure of microtubules and
motor proteins that translate energy from ATP cycles into a complex fluid
flow. Although this process is vital for intracellular transport of nutri
ents\, a quantitative mathematical model for this system remains elusive.
Recent experimental work has produced high-resolution video of this system
and made possible attempts to derive a model directly from data. In this
poster\, I will discuss the application of a data-driven model discovery m
ethod called ”PDE-Find” to this complex system. I will describe the ac
curacy and robustness of PDE-Find for the simplified task of reconstructin
g a proposed model from simulation data and discuss the corresponding chal
lenges. I will also propose methodologies for overcoming those challenges
and future steps to utilize the experimental data.\n\nhttps://indico.mpi-m
agdeburg.mpg.de/event/7/contributions/165/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/165/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Extrapolating Nuclear Masses using Bayesian Gaussian Process Regre
ssion
DTSTART;VALUE=DATE-TIME:20200727T173000Z
DTEND;VALUE=DATE-TIME:20200727T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-162@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Rahul Jain (Michigan State University )\nThe mass of
a nucleus is its fundamental quantity. It dictates the stability of a par
ticular nucleus\, the type of decays and nuclear reactions it can undergo\
, and much more. Yet after decades of experimental efforts\, we are unable
to experimentally measure the masses of thousands of exotic isotopes. The
y cannot be produced in the laboratory so we have to rely on theoretical m
odels. However\, more than a dozen different physics-based models predict
very different values for extrapolated nuclear masses because of different
assumptions\, missing physics\, etc. in each of them. We use a data-drive
n approach to predict the masses of these exotic isotopes by modeling the
residuals\, i.e. the difference between the experimental masses and theore
tically predicted masses accounting for the missing piece in theoretical m
odels. In particular\, we use Bayesian Gaussian Process Regression that al
so provides credibility intervals on our predictions and helps in uncertai
nty quantification. We further use Bayesian Model Averaging to combine the
predictive powers of different models and also account for model selectio
n uncertainty.\n\nhttps://indico.mpi-magdeburg.mpg.de/event/7/contribution
s/162/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/162/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Learning from Data for Traffic Control
DTSTART;VALUE=DATE-TIME:20200729T173000Z
DTEND;VALUE=DATE-TIME:20200729T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-160@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Urs Baumgart (Fraunhofer ITWM)\nData-driven methods
are a promising approach for optimizing traffic control systems. Today’s
vehicle technology allows to collect an increasing amount of data to impr
ove the vehicles’ performance\, reliability and safety. Concerning mobi
lity infrastructure and communication technology\, larger and larger datas
ets can be transmitted faster every year. Our goal is to use (real-time) d
ata\, communicated between cars and infrastructure\, to improve traffic fl
ow in the future and to support holistic\, efficient and sustainable mobil
ity solutions.\n\nWe therefore model different networks using a microscopi
c traffic simulation where Reinforcement Learning (RL) methods are used to
let agents (vehicles) learn to drive more fluently through typical traffi
c situations. The agents obtain real-time information from other vehicles
and learn to improve the traffic flow by repetitive observation and algori
thmic optimization. Accordingly\, we use RL to control traffic guidance sy
stems\, such as traffic lights. In [1]\, an illustrating example is given\
, where the traffic light system of the “Opel roundabout”\, Kaiserslau
tern’s largest roundabout\, is considered in a model – it has been set
up and improved by Reinforcement Learning. As underlying model structures
for all RL approaches\, we use\, e.g.\, linear models\, radial-basis func
tion networks and neural nets. In the future we plan to investigate the pe
rformance of other model variants\, such as Gaussian Processes\, and we wi
ll enhance this model-free approach with physics-based microscopic traffic
models to improve the mathematical description of the underlying dynamica
l system.\n\n[1] U. Baumgart. *Reinforcement Learning for Traffic Control*
. Master’s Thesis\, University of Mannheim\, 2019.\n\nhttps://indico.mpi
-magdeburg.mpg.de/event/7/contributions/160/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/160/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Multipopulation mortality rates modelling and forecasting: The mul
tivariate functional principal component analysis approach
DTSTART;VALUE=DATE-TIME:20200729T173000Z
DTEND;VALUE=DATE-TIME:20200729T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-216@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Ka Kin Lam (University of Leicester)\nHuman mortalit
y patterns and trajectories in closely related subpopulation are likely li
nked together and share similarities. It is always desirable to model them
simultaneously while taking their heterogeneity into account. This poster
introduces two new models for jointly mortality modelling and forecasting
of multiple subpopulations in adaptations of the multivariate functional
principal component analysis techniques. The first model extends the class
ical independent functional data model to a multi-population modelling set
ting. The second one is a natural extension of the first model in a cohere
nt direction. Its design primarily fulfils the idea that when several sub-
population groups have similar socio-economic conditions or common biologi
cal characteristics and such these close connections are expected to evolv
e in a non-diversifying fashion. We demonstrate the proposed methods by us
ing sex-specific mortality data of Japan. Their forecast performances are
then further compared with several existing models\, including the indepen
dent functional data model and the product-ratio model\, through a compari
son with mortality data of ten developed countries. Our experiment results
show that the first proposed model maintains a comparable forecast abilit
y with the existing methods. In contrast\, the second proposed model outpe
rforms the first model as well as the current models\, in terms of forecas
t accuracy\, plus several desirable properties.\n\nhttps://indico.mpi-magd
eburg.mpg.de/event/7/contributions/216/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/216/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Deep learning of multibody minimal coordinates for estimation
DTSTART;VALUE=DATE-TIME:20200729T173000Z
DTEND;VALUE=DATE-TIME:20200729T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-166@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Andrea Angeli (KU Leuven\, Flanders Make)\nMultibody
systems are the state-of-the-art tool to model complex mechanical mechani
sms. However\, they typically include redundant coordinates plus constrain
ts\, leading to differential algebraic equations for the dynamics which re
quire dedicated integration schemes and control/estimation algorithms.\nIn
my work\, autoencoder neural networks are combined with the multibody phy
sics information. In this way\, the autoencoder does not only perform a di
mensionality reduction of the original coordinates but can be used for a m
odel order reduction obtaining a reduced-order model where the dynamics is
expressed with ordinary differential equations and standard estimation al
gorithms can be used.\nThis permits to combine the physics-informed neural
network with measurements in order to estimate unknown parameters or inpu
ts in the system\, for instance with an extended Kalman filtering scheme.\
n\nhttps://indico.mpi-magdeburg.mpg.de/event/7/contributions/166/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/166/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Basis Generation Techniques for Symplectic Model Order Reduction
DTSTART;VALUE=DATE-TIME:20200730T110000Z
DTEND;VALUE=DATE-TIME:20200730T120000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-152@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Patrick Buchfink (University of Stuttgart)\nMathemat
ical models for physical phenomena typically show certain structures if fo
rmulated correctly. Hamiltonian systems are an example for such structured
systems. They rely on the so-called symplectic structure\, which is respo
nsible for the characteristic property to preserve the Hamiltonian functio
n over time. In numerical mathematics\, preservation of these structures s
hows great improvements in stability and accuracy e.g. for numerical integ
ration [1] or model order reduction (MOR) [2].\n\nOur goal is to show how
so-called symplectic reduced-order bases can be computed from data\, which
is relevant for structure-preserving MOR of Hamiltonian systems. To this
end\, we give a short introduction to symplecticity and Hamiltonian system
s. Based thereon\, we discuss symplectic basis generation techniques in co
mparison to the classical Proper Orthogonal Decomposition (also: Principal
Component Analysis). Based on a two- and a three-dimensional linear elast
icity model\, we show how such techniques can be used (a) for classical da
ta compression and reconstruction tasks and (b) for symplectic MOR.\n\n[1]
E. Hairer\, G. Wanner\, and C. Lubich. Geometric Numerical Integration. S
pringer\, Berlin\, Heidelberg\, 2006. ISBN 978-3-540-30666-5. doi: 10.1007
/3-540-30666-8.\n\n[2] L. Peng and K. Mohseni. Symplectic Model Reduction
of Hamiltonian Systems. SIAM J. Sci. Comput.\, 38(1):A1–A27\, 2016. doi:
10.1137/140978922.\n\nhttps://indico.mpi-magdeburg.mpg.de/event/7/contrib
utions/152/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/152/
END:VEVENT
BEGIN:VEVENT
SUMMARY:System Identification by Sparse Bayesian Learning
DTSTART;VALUE=DATE-TIME:20200727T173000Z
DTEND;VALUE=DATE-TIME:20200727T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-164@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Luning Sun (University of Notre Dame)\nSystem identi
fication from noisy data is challenging in many science and engineering fi
elds. In current work\, we present an approach of system identification by
sparse Bayesian learning methods. The key idea is to determine the sparse
relevant weights from a constructed library by learning from noisy data.
The sparse promoting prior is used to regularize the learning process. Fur
thermore\, to identify a parsimonious system\, the sequential threshold tr
aining is incorporated into sparse Bayesian learning. It is especially hel
pful when the learned data has large noise. Furthermore\, we extend our ap
proach to learn a parametric system by using group sparsity. Several expli
cit and implicit ODE/PDE systems are used to demonstrate the effectiveness
of this method.\n\nhttps://indico.mpi-magdeburg.mpg.de/event/7/contributi
ons/164/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/164/
END:VEVENT
BEGIN:VEVENT
SUMMARY:One size does not fit all: Parameterized biomechanical models for
crashworthiness simulations
DTSTART;VALUE=DATE-TIME:20200729T173000Z
DTEND;VALUE=DATE-TIME:20200729T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-168@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Göktürk Kuru (Siemens Digital Industries Software)
\nhttps://indico.mpi-magdeburg.mpg.de/event/7/contributions/168/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/168/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Physics Guided Deep-Learning Based Nonlinear Reduced Order Model f
or Aeroelastic Applications
DTSTART;VALUE=DATE-TIME:20200730T110000Z
DTEND;VALUE=DATE-TIME:20200730T120000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-211@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Rahul Halder (National University of Singapore)\nThi
s study aims to model transonic airfoil-gust interaction and the gust resp
onse on transonic aileron-buzz problems using high fidelity computational
fluid dynamics (CFD) and the Long Short-Term Memory (LSTM) based deep lear
ning approach. It first explores the rich physics associated with these in
teractions\, which show strong flow field nonlinearities arising from the
complex shock-boundary layer interactions using CFD. In the transonic reg
ime\, most linear Reduced Order Models (ROMs) fail to reconstruct the unst
eady global parameters such as the lift\, moment and drag coefficients and
the unsteady distributive flow variables such as velocity\, pressure\, an
d skin friction coefficients on the airfoil or in the entire computational
domain due to the nonlinear shock-gust interaction. As it is well known t
hat a deep-learning framework creates several hypersurfaces to generate a
nonlinear functional relationship between the gust or structural input and
the unsteady flow variables as an output an algorithm is proposed to over
come the limitations of linear ROMs. This algorithm consists of two integr
al steps\, namely a dimensionality reduction where the Discrete Empirical
Interpolation Method (DEIM) based linear data compression approach is appl
ied and the reduced state is trained using the LSTM based Recurrent Neural
Network (RNN) for the reconstruction of unsteady flow variables. Current
study further modifies the loss function inside the LSTM network using the
residual from the Navier Stokes equation and propose a Physics guided LST
M network. The present work shows its potential for predicting transonic
airfoil gust response and the aileron buzz problem demonstrating several o
rders of computational benefit as compared to high fidelity CFD.\n\nhttps:
//indico.mpi-magdeburg.mpg.de/event/7/contributions/211/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/211/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lecture/exercises 3
DTSTART;VALUE=DATE-TIME:20200729T160000Z
DTEND;VALUE=DATE-TIME:20200729T173000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-64@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: J. Nathan Kutz (University of Washington)\nIntroduct
ion to neural networks for DMD & Koopman approximations\n- NN for learning
coordinate transformations\n- Koopman reductions more linear ROMs\n\nhttp
s://indico.mpi-magdeburg.mpg.de/event/7/contributions/64/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lecture/exercises 1
DTSTART;VALUE=DATE-TIME:20200727T120000Z
DTEND;VALUE=DATE-TIME:20200727T133000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-72@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Feliks Nüske (Paderborn University)\nIntroduction t
o Stochastic Dynamics and Transition Operators\n- Markov Property and Tran
sition Kernels\n- Perron-Frobenius and Koopman Operator\n- Examples (ODEs\
, Brownian Motion)\n- Stationarity\, Reversibility\n\nhttps://indico.mpi-m
agdeburg.mpg.de/event/7/contributions/72/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lecture/exercises 3
DTSTART;VALUE=DATE-TIME:20200729T120000Z
DTEND;VALUE=DATE-TIME:20200729T133000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-74@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Feliks Nüske (Paderborn University)\n(E)DMD for Sto
chastic Dynamics\n- Basic EDMD\n- Variational Principle for Reversible Dyn
amics\n- Generator EDMD\n\nhttps://indico.mpi-magdeburg.mpg.de/event/7/con
tributions/74/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A Hamiltonian Monte Carlo Bayesian Inference Approach Using Deep L
earning for Modeling Metabolism
DTSTART;VALUE=DATE-TIME:20200729T173000Z
DTEND;VALUE=DATE-TIME:20200729T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-171@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Christina Schenk (Basque Center for Applied Mathemat
ics)\nMetabolism plays a key role in a multitude of different biological p
rocesses ranging from food production and biofuel production to human heal
th. Predicting the metabolism of a living organism\, however\, can be a ch
allenging task. Genome-scale models (GEMs) can provide this predictive pow
er by accounting for all metabolic reactions in an organism's genome. So f
ar\, GEMs have been used to model metabolism through optimization approach
es\, but this approach shows limitations. We propose a new approach based
on a combination of Markov Chain Monte Carlo and Bayesian inference that p
rovides all metabolic states compatible with the available experimental da
ta. We discuss efficient sampling techniques which can leverage high perfo
rmance computing to efficiently handle the associated computational burden
. These techniques are based on Hamiltonian Monte Carlo methods that lever
age artificial neural networks for efficient gradient calculation. The cor
responding numerical results for case studies related to predictive modeli
ng of metabolism are presented and analyzed. This technique represents a f
irst step towards modeling microbial communities in the future.\n\nhttps:/
/indico.mpi-magdeburg.mpg.de/event/7/contributions/171/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/171/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Real-time virtual acoustics using physics-informed data-driven tec
hniques
DTSTART;VALUE=DATE-TIME:20200729T173000Z
DTEND;VALUE=DATE-TIME:20200729T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-170@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Finnur Pind (Technical University of Denmark)\n‘Vi
rtual Acoustics’ is the field of science that deals with simulating and
synthesizing sound in virtual domains. The areas of application are widesp
read\, e.g.\, building design\, virtual entertainment and hearing research
. The problem is extremely challenging because it involves simulating time
-dependent wave propagation over a broad frequency spectrum in large and c
omplex domains – ideally under real-time constraints. In our previous wo
rk\, we have developed a high-fidelity massively parallel DGFEM based acou
stics simulator and a method for exploring pre-computed simulation results
in an audio-visual virtual reality experience for static scenes. However\
, the ultimate goal is to perform the simulations in real time\, thus allo
wing for interactive and dynamic scenes in the VR. Our future research wil
l be to explore whether physics-informed\, data-driven surrogate modelling
techniques can be applied to solve the problem under real-time constraint
s. We will pursue a combination of reduced basis techniques and efficient
data-driven surrogate modeling. In such a setup\, one leverages the high c
omputational efficiency of the reduced basis model to create a large label
ed data set\, which serves to train the surrogate model based on Gaussian
Process Regression or\, alternatively\, a feed forward Neural Network in a
simple supervised learning approach. Our hope is that the evaluation of s
uch surrogate models is extremely efficient and that this will provide the
last step to reach the required acceleration to enable real-time or near
real-time performance.\n\nhttps://indico.mpi-magdeburg.mpg.de/event/7/cont
ributions/170/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/170/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lecture/exercises 4
DTSTART;VALUE=DATE-TIME:20200730T140000Z
DTEND;VALUE=DATE-TIME:20200730T153000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-70@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Benjamin Peherstorfer (New York University)\n- Inter
polatory model reduction: transfer function\, H2 norm\, Loewner\n- Learnin
g in the frequency domain: Loewner noise\, AAA\, vector fitting\n\nhttps:/
/indico.mpi-magdeburg.mpg.de/event/7/contributions/70/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Machine learning for parameters identification in structural joint
s models
DTSTART;VALUE=DATE-TIME:20200727T173000Z
DTEND;VALUE=DATE-TIME:20200727T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-172@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Simone Gallas (KU Leuven\, Department of Mechanical
Engineering\, Division LMSD\; Core Lab DMMS-D\, Flanders Make)\nIn the con
text of multi-material lightweight assemblies\, structural joints such as
adhesives and bolts should be taken into account in the FE models for a re
liable representation of the reality. The goal of this research work is to
identify the parameters of the joints models exploiting the potential of
the Virtual Sensing techniques.\nParameters identification can be achieved
via the minimization of the error between model results and experimental
results. In the current research work\, a parametric-reduced model and a s
et of measurements are combined in a stochastic estimator such as an Exten
ded Kalman filter\, that tracks the dynamic states and parameters of the a
ssembly under investigation. \nIn the next steps\, Machine Learning approa
ches will be investigated in view of a benchmarking with the current metho
ds\, but also in view of an integration between them. Machine Learning wil
l be used to define new surrogate models\, able to mimic the relation betw
een the physics-inspired model parameters (to be later identified) and pro
duct performance. According to this scheme\, the physics-inspired models w
ill be used to produce a set of training data for the Machine Learning alg
orithm\, and the resulting surrogate model will be used in the above-menti
oned parameter identification schemes.\n\nhttps://indico.mpi-magdeburg.mpg
.de/event/7/contributions/172/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/172/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Machine learning for parameter identification and model reduction
of gradient-enhanced damage models for metal forming processes
DTSTART;VALUE=DATE-TIME:20200729T173000Z
DTEND;VALUE=DATE-TIME:20200729T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-173@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Robin Schulte (Institute of Mechanics\, TU Dortmund
University)\nUntil now\, only classical approaches for the parameter ident
ification of gradient-enhanced damage models combined with e.g. finite pla
sticity or rate-dependent phenomena are used in order to characterize the
damage evolution in metal forming processes. In the future\, the models wi
ll be extended to simulate hot forming processes. Considering the increasi
ngly complex material models with significant numbers of parameters\, the
capabilities of machine learning techniques shall be examined for this app
lication. Later on\, considering the complex boundary value problems of th
e different processes\, model reduction will be used to decrease the compu
tational cost of the finite element simulations while maintaining the accu
racy of micro-mechanical material models to characterize the damage evolut
ion in the processes. Therefore\, a neural network will be trained with th
e constitutive response of the micro-mechanical material models.\n\nhttps:
//indico.mpi-magdeburg.mpg.de/event/7/contributions/173/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/173/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Model adaptation for hyperbolic balance laws employing constraint
aware neural networks
DTSTART;VALUE=DATE-TIME:20200729T173000Z
DTEND;VALUE=DATE-TIME:20200729T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-175@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Hrishikesh Joshi (Technical University of Darmstadt)
\nPhysical phenomena like chemically reacting flows are computationally ex
pensive to simulate due to the interaction between different physics at a
wide range of time and length scales. Chemically reacting flows can be des
cribed by systems of hyperbolic partial differential equations with stiff
source terms. The governing equations can be simplified by assuming chemic
al equilibrium and then it is possible to replace the full system with a s
impler system. We investigate model adaptation for such systems. The model
adaptation is carried out between the full system of equations referred t
o as the complex system and the simple system\, which is obtained by proje
cting the complex system on to the equilibrium manifold. When numerically
solving the simple system\, to compute the flux a mapping from the state s
pace of the simple system to the state space of the complex system needs t
o be employed. This involves solving a computationally expensive non-linea
r system of equations. To further reduce the computational expenses needed
when solving the simple system\, the mapping employed in the simple syste
m can be replaced by an approximate mapping\, which has to be constructed
by accounting for the physics behind the mapping. Such an approximate mapp
ing can be constructed employing machine learning techniques like physics
based or constraint aware neural networks. Model adaptation is carried out
by decomposing the computational domain in space and time and then the co
mplex model is employed where necessary and the simple system\, employing
the machine learned approximate mapping\, where sufficient. The domain dec
omposition is carried by constructing a posteriori error estimates which t
ake in to account the discretization\, modeling errors and errors incurred
due to employing the approximate mapping.\n\nhttps://indico.mpi-magdeburg
.mpg.de/event/7/contributions/175/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/175/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Analytical and Learning Model of a Hybrid-Fluidic Elastomer Actuat
or for Reliable Control and Perturbation Detection
DTSTART;VALUE=DATE-TIME:20200727T173000Z
DTEND;VALUE=DATE-TIME:20200727T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-174@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Uksang Yoo (The University of Texas at Austin)\nWe a
re developing a pneumatic Hybrid-Fluidic Elastomer Actuator (H-FEA) by com
bining an additively manufactured internal structure and silicone elastome
r. It is evident that in many soft robotic applications\, there is a need
to be able to sense shape of the robot and collision with the environment.
To address these needs\, we are developing an analytical model of the non
linear kinematics of the H-FEA with internal energy-based models that comb
ine both the linear and nonlinear components of the H-FEA. Using the analy
ical model\, we are able to determine the shape of the actuator given the
internal pressure. To extend this model and detect external perturbations
in obstructed environments\, we propose to use a probabilistic learning mo
del. This learning model is trained on mapping of the input volume to dete
rmine perturbation or collision probability at the state given by the anal
ytical model.\n\nhttps://indico.mpi-magdeburg.mpg.de/event/7/contributions
/174/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/174/
END:VEVENT
BEGIN:VEVENT
SUMMARY:An optimization-based approach for the reduction of parametrized c
onservation laws with discontinuities
DTSTART;VALUE=DATE-TIME:20200727T173000Z
DTEND;VALUE=DATE-TIME:20200727T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-191@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Marzieh Alireza Mirhoseini (University of Notre Dame
)\nPartial differential equations (PDEs) are commonly used to model comple
x systems in applied sciences. Methods for estimating PDE parameters requi
re repeatedly solving PDEs numerically under thousands of candidate parame
ter values\, and thus the computational load is high and expensive. To mak
e these problems tractable we use reduced-order models (ROMs) to reduce th
e computational cost of PDE solves. PDE models of fluid flow or other any
advection dominated physics may produce a discontinuous solution. We will
construct a bijection that aligns features in a fixed reference domain suc
h that snapshots have jump locations at the same coordinates\, independent
of the parameters. We are proposing a procedure to align features in the
reference domain because this will improve (increase) the N-widths decay a
nd explicitly deal with discontinuities in the construction and definition
of the ROM. To perform the alignment\, we convert the discretized conserv
ation law into a PDE-constrained optimization problem. We build a projecti
on-based ROM in the reference domain where discontinuities are aligned. It
is our goal at the offline stage during which computationally expensive t
raining tasks compute a representative basis for the system state. Then\,
during the inexpensive online stage\, we solve an optimization problem to
compute approximate solutions for an arbitrary parameter. The solution of
a new parameter would be aligned in the reference domain with the rest of
the parameters encountered during the offline stage.\n\nhttps://indico.mpi
-magdeburg.mpg.de/event/7/contributions/191/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/191/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enhancing battery recharge performance by combined Machine Learnin
g and PDE modelling
DTSTART;VALUE=DATE-TIME:20200730T110000Z
DTEND;VALUE=DATE-TIME:20200730T120000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-176@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Angela Monti (University of Salento)\nMy PhD researc
h concerns mathematical modelling\, numerical simulations and applications
to electrochemical energy storage devices\, in particular Zn-air batterie
s (ZAB).\nZn-air battery (ZAB) concepts exhibit storage potentialities ran
ging from low-power portable consumer electronics\, to automotive and home
applications (see [2]). During recharge\, the regeneration of Zn is howev
er daunted by severe morphological changes leading to low cycle life. Thes
e morphological changes are related to metal growth instabilities. \nThe m
ain goal of the project is to set up a research framework aimed at attacki
ng such battery electrode problems with a Machine Learning (ML) approach b
ased on a Training Set of data resulting from numerical solutions of a rea
ction-diffusion PDE model\, that is able to capture the essential features
of unstable material growth in electrochemical systems by means of the so
-called Turing patterns (see [1\,2\,3] and reference therein).\nIn this me
soscopic model\, referred to as the “DIB model"\, the recharge instabili
ty is controlled by the interaction between material “shape" and materia
l “chemistry"\; the source terms include the physics describing the grow
th process and the parameters involved account for the battery operating c
onditions (chiefly electrolyte chemistry and charge rate). One of the key
results of the analysis of the model [3\,4\,5] is the correlation of the v
alues of the model parameters with the occurrence and type of growth insta
bilities. In particular\, in [3] a segmentation of the parameter space in
morphological classes has been proposed (see [6]). \n\nThe first applicati
on I am planning is to train the ML algorithm with a computed set of morph
ological maps\, and to use it to classify a set of experimental maps\, obt
ained by optical microscopy observations of electrodeposited alloys.\n\n\n
REFERENCES\n[1] Lacitignola D\, Bozzini B\, Sgura I- Spatio-temporal organ
ization in a morphochemical electrodeposition model: Hopf and Turing insta
bilities and their interplay\, European Journal of Applied Mathematics (20
15) 26(2) 143-173\, dx.doi.org/10.1017/S0956792514000370\n[2] Bozzini B\,
Mele C\, D'Autilia MC\, Sgura I. - Dynamics of zinc-air battery anodes: An
electrochemical and optical study complemented by mathematical modelling\
, Metallurgia Italiana (2019) 111(7-8)\, 33-40\n[3] Lacitignola D\, Bozzin
i B\, Frittelli M\, Sgura I- Turing pattern formation on the sphere for a
morphochemical reaction-diffusion model for electrodeposition\, Communicat
ions in Nonlinear Science and Numerical Simulation (2017) 48\, 484-508\, d
x.doi.org/10.1016/j.cnsns.2017.01.008\n[4] Sgura I\, Lawless A\, Bozzini B
- Parameter estimation for a morphochemical reaction-diffusion model of e
lectrochemical pattern formation\, Inverse Problems in Science and Enginee
ring (2019) 27(5)\, 618-647 doi.org/10.1080/17415977.2018.1490278\n[5] Sgu
ra I\, Bozzini B - XRF map identification problems based on a PDE electrod
eposition model\, Journal of Physics D: Applied Physics (2017) 50(15)\, dx
.doi.org/10.1088/1361-6463/aa5a1f\n[6] https://www.researchgate.net/figure
/Segmentation-of-the-Turing-region-six-subregions-R-0-R-1-R-5-from-top-to-
bottom_fig4_326338358\n\nhttps://indico.mpi-magdeburg.mpg.de/event/7/contr
ibutions/176/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/176/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Towards Deep Learning Based Controllers with Nominal Closed Loop S
tability Guarantees
DTSTART;VALUE=DATE-TIME:20200729T173000Z
DTEND;VALUE=DATE-TIME:20200729T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-180@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Hoang Hai Nguyen (Otto-von-Guericke University Magde
burg\, Magdeburg\, Germany)\nDeep learning approaches are widely used for
many tasks and applications\, spanning from object detection\, to classifi
cation and control. Certifying or enforcing performance and stability guar
antees for controllers based on deep learning is\, however\, challenging.
This work considers the use of so called non-autonomous input-output st
able deep neural networks for the control of dynamical systems. We train
the neural network based on an existing controller that achieves desirabl
e nominal closed loop system properties. Assuming the infinite layer netwo
rk leads to a stable closed loop\, we derive bounds for the finite number
of layers of the neural network\, such that stability of the nominal close
d loop system under the deep network controller is guaranteed. We furtherm
ore derive conservative conditions which can be easily integrated in the l
earning phase to enforce stability based on the small gain theorem. The re
sults are underlined by a simulation study considering the control of a co
ntinuously stirred tank reactor.\n\nhttps://indico.mpi-magdeburg.mpg.de/ev
ent/7/contributions/180/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/180/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stochastic frequency domain surrogate models for linear structural
dynamics
DTSTART;VALUE=DATE-TIME:20200730T110000Z
DTEND;VALUE=DATE-TIME:20200730T120000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-203@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Felix Schneider (Technical University of Munich)\nWh
en conducting measurement on existing structures\, e.g. collecting the tim
e-response of a building\, and trying to compute the same response by a su
itable computational method\, one often notices discrepancies between the
measurement and model data. These discrepancies are due to a wide range of
errors\, done in both the measurement and the modelling. The model errors
can stem from uncertainty in the model parameters and\, often more import
antly\, the model error itself. \nOne can then use stochastic methods to o
btain a more robust response prediction of the structure at hand (forward
Uncertainty Quantification (UQ)) and use the data gathered to learn about
the model parameters and the errors involved in the modelling (Inverse UQ)
. Often\, Bayesian methods are applied to solve the inverse problem at han
d. In any case\, applying sampling-based approaches to UQ requires the rep
eated evaluation of the model and can become infeasible for computationall
y demanding models. \nTo address this issue we introduced a novel surrogat
e model that is especially suitable for approximating linear structural dy
namic models in the frequency domain (Schneider et al. 2020). The surrogat
e approximates the original model by a rational of two polynomial chaos ex
pansions (PCE) over the stochastic input space. The complex coefficients i
n the expansions are obtained by solving a regression problem in a non-int
rusive manner. \nOne drawback in the PCE based surrogate model is the fact
orial growth of the number of basis terms in the expansions with the numbe
r of input dimensions and polynomial order\, known as the curse of dimensi
onality. To circumvent this restriction\, often approaches that find spars
e bases representations are applied. One of these approaches is Sparse Bay
esian Learning (Tipping\, 2001). Implementing such an approach for the rat
ional surrogate model could help in obtaining a sparse and thus efficient
surrogate model for UQ in the frequency domain.\nFurther improvements to t
he method include extending the approach to work with vector-valued output
in an efficient manner\, as now\, the surrogate is only able to approxima
te scalar model output. Promising approaches include Proper Generalized De
composition (PGD) (Chevreuil et al. 2012)\, among others. \nReferences:\n[
1] Schneider\, F.\, Papaioannou\, I.\, Ehre\, M.\, & Straub\, D. (2020). P
olynomial chaos based rational approximation in linear structural dynamics
with parameter uncertainties. Computers & Structures\, 233\, 106223.\n[2]
Chevreuil\, M.\, & Nouy\, A. (2012). Model order reduction based on prope
r generalized decomposition for the propagation of uncertainties in struct
ural dynamics. International Journal for Numerical Methods in Engineering\
, 89(2)\, 241-268.\n[3] Tipping\, M. E. (2001). Sparse Bayesian learning a
nd the relevance vector machine. Journal of machine learning research\, 1(
Jun)\, 211-244.\n\nhttps://indico.mpi-magdeburg.mpg.de/event/7/contributio
ns/203/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/203/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Convolutional Neural Networks for object detection in professional
appliances
DTSTART;VALUE=DATE-TIME:20200729T173000Z
DTEND;VALUE=DATE-TIME:20200729T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-148@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Laura Meneghetti (SISSA)\nIn the context of industri
al applications involving machine learning techniques\, a challenging pro
blem is represented by object detection\, as can be seen in [1]. A particu
lar application of it inside a leading company in the field of professiona
l appliances\, such as Electrolux Professional\, is represented by the rec
ognition and localization of different types of objects.\nA possible appro
ach to deal with object detection problems is represented by Artificial Ne
ural Networks (ANN) and in particular by Convolutional Neural Networks (CN
N). In order to solve this issue\, we need to handle with two different ta
sks: classification and localization. The particular architecture of the e
xisting CNNs is useful to extract the low-level features of the objects (i
.e. edges\, lines\, …)\, but it is not enough to cope also with the prob
lem of finding their position in a picture. Therefore\, some extra layers
must be added on the top of a chosen CNN in order to detect the high-level
features\, such as the position.\nWe have decided to study mainly two sta
te-of-the-art meta-architectures: Faster Region Based Convolutional Neural
Network (Faster R-CNN) [3] and Single Shot Detector (SSD) [2]\, because t
he first is very accurate\, whereas the second is very fast. Since our alg
orithm have to be included in a professional appliance\, the computing tim
e needed to detect a new object has to be as fast as possible (ideally rea
l-time). Hence\, in this work we will make a comparison between the two ar
chitectures in terms of speed and accuracy\, proposing at the same time a
new strategy for the construction of the training batches using an unsuper
vised approach.\n\nReferences\n\n[1] Goodfellow\, I.\, Bengio Y. and Courv
ille A.\, 2016\, Deep Learning. MIT Press.\n[2] Liu W.\, Anguelov D.\, Erh
an D.\, Szegedy C.\, Reed S.\, Fu C.-Y. and C. Berg A.\, 2016\, SSD: Singl
e Shot MultiBox Detector.\n[3] Ross S.\, He K.\, Girshick R.\, and Sun J.\
, 2015\, Faster R-CNN: Towards Real-Time Object Detection with Region Prop
osal Networks. Advances in Neural Information Processing Systems.\n\nhttps
://indico.mpi-magdeburg.mpg.de/event/7/contributions/148/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/148/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Analytical Modeling and Evaluation of Curvature-Dependent Distrib
uted Friction Force in Tendon-Driven Continuum Manipulators
DTSTART;VALUE=DATE-TIME:20200727T173000Z
DTEND;VALUE=DATE-TIME:20200727T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-179@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Yang Liu (The University of Texas at Austin)\nTendon
-Driven Continuum Manipulators (TD-CMs) have gained increasing popularity
in various minimally invasive surgical robotic applications. However\, the
adverse effects of tendon-sheath friction along the transmission path may
result in significant non-uniform cable tension and subsequently motion l
osses\, which affects the deformation behavior of a TD-CM. Most of the cur
rent approaches for modeling friction have been mainly developed based on
either simplifying assumptions (e.g.\, constant-curvature deformation beha
vior or point load friction forces) or experimentally-tuned lumped models
that are not extendable to a generic deformation behavior for a VC-CM. We
propose developing a physics-based modeling approach for modeling deformat
ion behavior of a TD-CM by extending the typical geometrically exact model
based on the Cosserat rod theory and include the effect of Curvature-Depe
ndent Distributed Friction Force (CDDF) between the tendon and sheath.\n\n
https://indico.mpi-magdeburg.mpg.de/event/7/contributions/179/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/179/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Learning the Interfacial Area Equation from Data
DTSTART;VALUE=DATE-TIME:20200727T173000Z
DTEND;VALUE=DATE-TIME:20200727T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-178@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Stephen Chen (University of California San Diego)\nT
he ability for sparse symbolic machine learning techniques to discover gov
erning equations from data [1]\, [2] has opened up many opportunities in f
luid mechanics. The equations solved in fluid mechanics are conservation
of mass\, momentum\, and energy as well as the closure models. Closure mo
dels arise from averaging the conservation equations. Averaging introduce
s additional terms\, which require additional equations\, termed closure m
odels\, to solve. It is in discovering the equations governing the closur
e models that sparse symbolic machine learning is most useful. Closure mo
dels are not based upon strict physical laws\, but on experimental data an
d engineering judgement. This makes them ideal for machine learning techn
iques. Moreover\, sparse symbolic machine learning has an advantage over
previous neural network approaches\, [3]\, in that the output can be easil
y integrated into existing computer codes\, with an understanding of how i
t will extrapolate to untrained conditions. There has already been quite
a bit of attention to using sparse symbolic learning for turbulence closur
e models [4]–[6]. Similar things are possible for two-phase flow. \n\
nTwo-phase flows are typically modeled using the two fluid model\, [7]\, [
8]\, in which each phase is modeled as a continua and has its own set of c
onservation equations (mass\, momentum\, and energy)\, and the phases are
coupled by interfacial transfer terms. The interfacial transfer terms req
uire closure models. The current state of the art for nuclear reactor sys
tem codes (RELAP\, TRACE\, CATHARE) is for the interfacial transfer terms
to be correlated in terms of the flow regime. In two phase flow\, the flo
w regime describes the topology of the flow\, i.e. whether the gas forms b
ubbles inside the liquid (bubbly flow) or whether the liquid is confined t
o the walls and as droplets inside the gas core (annular flow). The flow
regime transitions themselves are also empirically correlated. It has bee
n noted that the interfacial transfer closures can be written in terms of
$a_i$\, the interfacial area per unit volume\, as (Interfacial transfer) =
$a_i$ x (Driving Force) [9]. Moreover\, the interfacial area changes dra
matically with the flow regime\, so if one could write an equation for the
interfacial area\, the empirical flow regime correlations could be dispen
sed with. Various derivations of an interfacial area equation have been p
erformed [10]–[12]\, the simplest of which [10] is:\n$ \\frac{\\partial
a_i}{\\partial t} = \\nabla \\cdot \\left( a_i v_i \\right) = \\sum_{j=1}^
{4} \\phi_j + \\phi_{ph} $\nIn this equation\, $\\phi_j$ represents the in
terfacial area rate of change due to coalescence or breakup\, and $\\phi_{
ph}$ represents the rate of change due to phase change. Attempts to valida
te this equation against high fidelity experimental data using the current
state of the art for models of $\\phi$ have noted that there are substan
tial issues once the flow regime moves beyond bubbly flow [13]. \n\nOur a
im is to use sparse machine learning to derive the governing equation for
the rate of interfacial area change. There are additional challenges when
attempting to learn multiphase as opposed to single phase flow closure mo
dels. The rate of interfacial area change must be learned from time resol
ved planar measurements\, which is the state of the art for experimental g
as liquid measurement techniques [14]. This is because multiphase DNS (di
rect numerical simulation) and LES (large eddy simulation) methods are not
developed enough to apply machine learning techniques directly on numeric
al data\, as was done to learn single phase turbulence closures [4]-[6].
However\, the benefit of an accurate interfacial area transport equation i
s the potential to dramatically improve nuclear reactor system codes and t
hereby nuclear reactor safety.\n\n[1] M. Schmidt and H. Lipson\, “Distil
ling free-form natural laws from experimental data\,” Science (80-. ).\,
vol. 324\, no. 5923\, pp. 81–85\, 2009\, doi: 10.1126/science.1165893.\
n[2] S. L. Brunton\, J. L. Proctor\, J. N. Kutz\, and W. Bialek\, “Disco
vering governing equations from data by sparse identification of nonlinear
dynamical systems\,” Proc. Natl. Acad. Sci. U. S. A.\, vol. 113\, no. 1
5\, pp. 3932–3937\, 2016\, doi: 10.1073/pnas.1517384113.\n[3] K. Duraisa
my\, G. Iaccarino\, and H. Xiao\, “Turbulence Modeling in the Age of Dat
a\,” Annu. Rev. Fluid Mech.\, vol. 51\, no. 1\, pp. 357–377\, 2019\, d
oi: 10.1146/annurev-fluid-010518-040547.\n[4] S. Beetham and J. Capecelatr
o\, “Formulating turbulence closures using sparse regression with embedd
ed form invariance\,” pp. 1–34\, 2020\, [Online]. Available: http://ar
xiv.org/abs/2003.12884.\n[5] M. Schmelzer\, R. P. Dwight\, and P. Cinnella
\, “Machine Learning of Algebraic Stress Models using Deterministic Symb
olic Regression\,” 2019\, [Online]. Available: http://arxiv.org/abs/1905
.07510.\n[6] M. Schmelzer\, R. Dwight\, and P. Cinnella\, “Data-driven d
eterministic symbolic regression of nonlinear stress-strain relation for R
ANS turbulence modelling\,” 2018 Fluid Dyn. Conf.\, 2018\, doi: 10.2514/
6.2018-2900.\n[7] J. E. Drew and S. L. Passman\, Theory of Multicomponent
Fluids\, vol. 59. 1998.\n[8] M. Ishii and T. Hibiki\, Thermo-Fluid Dynamic
s of Two-Phase Flow. 2006.\n[9] G. Kocamustafaogullari and M. Ishii\, “F
oundation of the interfacial area transport equation and its closure relat
ions\,” Int. J. Heat Mass Transf.\, vol. 38\, no. 3\, pp. 481–493\, 19
95\, doi: 10.1016/0017-9310(94)00183-V.\n[10] X. Y. Fu and M. Ishii\, “T
wo-group interfacial area transport in vertical air-water flow - I. Mechan
istic model\,” Nucl. Eng. Des.\, vol. 219\, no. 2\, pp. 143–168\, 2003
\, doi: 10.1016/S0029-5493(02)00285-6.\n[11] C. Morel\, N. Goreaud\, and J
. M. Delhaye\, “The local volumetric interfacial area transport equation
: Derivation and physical significance\,” Int. J. Multiph. Flow\, vol. 2
5\, no. 6–7\, pp. 1099–1128\, 1999\, doi: 10.1016/S0301-9322(99)00040-
3.\n[12] D. A. Drew\, “Evolution of geometric statistics\,” SIAM J. Ap
pl. Math.\, vol. 50\, no. 3\, pp. 649–666\, 1990\, doi: 10.1137/0150038.
\n[13] A. J. Dave\, A. Manera\, M. Beyer\, D. Lucas\, and M. Bernard\, “
Evaluation of two-group interfacial area transport equation model for vert
ical small diameter pipes against high-resolution experimental data\,” C
hem. Eng. Sci.\, vol. 162\, no. January\, pp. 175–191\, 2017\, doi: 10.1
016/j.ces.2017.01.001.\n[14] H. M. Prasser\, M. Misawa\, and I. Tiseanu\,
“Comparison between wire-mesh sensor and ultra-fast X-ray tomograph for
an air-water flow in a vertical pipe\,” Flow Meas. Instrum.\, vol. 16\,
no. 2–3\, pp. 73–83\, 2005\, doi: 10.1016/j.flowmeasinst.2005.02.003.\
n\nhttps://indico.mpi-magdeburg.mpg.de/event/7/contributions/178/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/178/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Analytical and Data-driven Models to Predict Algae Biofilm Growth
in Water Treatment
DTSTART;VALUE=DATE-TIME:20200727T173000Z
DTEND;VALUE=DATE-TIME:20200727T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-182@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Gerald Jones (Utah State University)\nHarmful algal
blooms (HABs) are a growing public health concern both nation and worldwid
e. Last year there were 25 major sites of HABs in the state of Utah alone.
These blooms are caused in part by excess nutrients (nitrogen and phospho
rus) being discharged from wastewater treatment plants (WWTPs). To combat
the growing prevalence of HABs the state of Utah is imposing new nitrogen
and phosphorus effluent standards for WWTPs. Utah State University is work
ing in collaboration with Central Valley Water Reclamation Facility (CVWRF
)\, the largest municipal WWTP in the state of Utah treating 60 million ga
llons per day\, and WesTech Engineering-Inc. to develop a novel biological
process to help WWTPs meet these new standards. This process is the rotat
ing algae biofilm reactor (RABR) that removes nutrients from wastewater by
producing algae biomass that can be used in bioproduct production. The RA
BR consists of disks rotating through a growth substrate (wastewater) to p
roduce an attached growth biofilm and remove nutrients from the substrate.
This biofilm can be mechanically harvested and converted into value-added
bioproducts including biofuels\, bioplastics\, animal feed\, and fertiliz
ers. Extensive research has been conducted on the RABR at laboratory and p
ilot scales\, but in preparation for scale-up and industrial applications
a mathematical model describing the system must be developed. Due to high
concentrations of nitrogen and phosphorus in the growth substrate and high
summertime light intensity\, the system is often light inhibited. An anal
ytical model has been adapted from work performed by Bara and Bonneford th
at describes light limited algae growth. This model will be augmented usin
g sparse identification of nonlinear dynamics (SINDy)\, a data-driven appr
oach allowing for the identification and development of important growth t
erms\, on data previously collected from the RABR at laboratory and pilot
scales along with data currently being collected.\n\nhttps://indico.mpi-ma
gdeburg.mpg.de/event/7/contributions/182/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/182/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kernel-based Active Subspaces with application to CFD problems usi
ng Discontinuous Galerkin method
DTSTART;VALUE=DATE-TIME:20200729T173000Z
DTEND;VALUE=DATE-TIME:20200729T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-183@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Francesco Romor (SISSA)\nThe need to devise model or
der reduction methods is strictly related to the finite nature of the avai
lable resources\, including the computational budget\, the amount of memor
y at disposal and the limited time\, which may range from a life-time to r
eal-time queries. Parametric studies\, from optimization tasks to the desi
gn of response surfaces\, suffer particularly from the curse of dimensiona
lity since they usually scale exponentially with the dimension of the para
meter space. A key pre-processing step is therefore reducing the dimension
of the space of parameters discovering some notion of low-dimensional str
ucture beneath. \n\nUnder mild regularity assumptions on the model functio
n of interest\, Active Subspaces have proven to be a versatile and benefic
ial method in engineering applications: from the shape-optimization of the
hull in naval engineering to model order reduction coupled with the reduc
ed basis method for the study of stenosis of the carotid. The procedure in
volved can be ascribed to gradient-based sufficient dimension reduction me
thods. In the context of approximation with ridge functions\, it finds the
oretical validation from the minimization of an upper bound on the approxi
mation error through the application of Poincaré-type inequalities and Si
ngular Value Decomposition (SVD). \n\nWe are going to present a possible e
xtension which address especially the linear nature of the Active Subspace
in search for a non-linear counterpart. The turning point comes from the
theory on Reproducing Kernel Hilbert Spaces (RKHS) which have been fruitfu
lly employed in machine learning to devise non-linear manifold learning al
gorithms such as Kernel Principal Component Analysis (KPCA). An essential
feature of the method that exploits the non-linear Active Subspaces should
be the flexibility to account for non-linear behaviours of the model func
tion.\n\nOur implementation is tested on toy-problems designed to exhibit
the strengths of the non-linear variant and on a benchmark with heterogene
ous parameters for the study of the lift and drag coefficients of a NACA a
irfoil. The numerical method applied for the approximation is the renowned
Discontinuous-Galerkin method. Future directions involve the developement
of other nonlinear extensions of the active subspaces method with deep ne
ural networks.\n\nhttps://indico.mpi-magdeburg.mpg.de/event/7/contribution
s/183/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/183/
END:VEVENT
BEGIN:VEVENT
SUMMARY:PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural
Networks for Solving Parametric PDEs on Irregular Domain
DTSTART;VALUE=DATE-TIME:20200727T173000Z
DTEND;VALUE=DATE-TIME:20200727T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-184@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Han Gao (University Of Notre Dame)\nRecently\, the a
dvent of deep learning has spurred interest in the development of physics-
informed neural networks (PINN) for efficiently solving partial differenti
al equations (PDEs)\, particularly in a parametric setting. Among all diff
erent classes of deep neural networks\, the convolutional neural network (
CNN) has attracted increasing attention in the scientific machine learning
community\, since the parameter-sharing feature in CNN enables efficient
learning for problems with large-scale spatiotemporal fields. However\, on
e of the biggest challenges is that CNN only can handle regular geometries
with image-like format (i.e.\, rectangular domains with uniform grids). I
n this paper\, we propose a novel physics-constrained CNN learning archite
cture\, aiming to learn solutions of parametric PDEs on irregular domains
without any labeled data. In order to leverage powerful classic CNN backbo
nes\, elliptic coordinate mapping is introduced to enable coordinate trans
forms between the irregular physical domain and regular reference domain.
The proposed method has been assessed by solving a number of PDEs on irreg
ular domains\, including heat equations and steady Navier-Stokes equations
with parameterized boundary conditions and varying geometries. Moreover\,
the proposed method has also been compared against the state-of-the-art P
INN with fully-connected neural network (FC-NN) formulation. The numerical
results demonstrate the effectiveness of the proposed approach and exhibi
t notable superiority over the FC-NN based PINN in terms of efficiency and
accuracy.\n\nhttps://indico.mpi-magdeburg.mpg.de/event/7/contributions/18
4/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/184/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Deep Neural Networks for Hyperbolic Conservation laws with Non-con
vex Flux
DTSTART;VALUE=DATE-TIME:20200729T173000Z
DTEND;VALUE=DATE-TIME:20200729T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-187@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Hadi Minbashian (Technical University of Darmstadt)\
nIn this work\, we investigate the capabilities of deep neural networks fo
r solving hyperbolic conservation laws with non-convex flux functions. The
behavior of the solution of these problems depends on the underlying smal
l scale regularization. In many applications concerning phase transition p
henomena\, the regularization terms consist of diffusion and dispersion wh
ich are kept in balance in the limit. This may lead to the development of
both classical and nonclassical (or undercompressive) shock waves at the s
ame time which makes finding the solution of these problems challenging fr
om both theoretical and numerical points of view. Here\, as a first step\,
we consider a scalar conservation law with cubic flux function as a toy m
odel and investigate the capabilities of physics-informed deep learning al
gorithms for solving this problem.\n\nhttps://indico.mpi-magdeburg.mpg.de/
event/7/contributions/187/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/187/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Data-driven Reduced Order Model of Flow-Induced Piezoelectric Ener
gy Harvesters
DTSTART;VALUE=DATE-TIME:20200730T110000Z
DTEND;VALUE=DATE-TIME:20200730T120000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-197@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Lan Shang (University of Luxembourg)\nPiezoelectric
energy harvesters (PEHs) are a potential alternative to batteries in large
-scale sensor networks and implanted health trackers\, but the low output
power and the narrow work range has been a bottleneck for its practical ap
plication. \n\nTo alleviate this problem\, the present research will devel
op a data-driven reduced-order model for flow-induced PEHs based on the da
taset obtained from a nonlinear and parametric electro-mechanical model.
This model will be a high-fidelity monolithic computational model establis
hed by the weighted residuals method and corresponding numerical solutions
will be calculated by the finite element method in FEniCS. Then a project
ion-based model order reduction will be implemented and machine learning w
ill be introduced to address challenges resulting from nonlinearity and mu
lti-parameters.\n\nOnce the reduced-order model is validated\, a reliable
and fast method to predict the performance of flow-induced PEHs will be ac
hieved\, promising real-time optimization of the design of PEHs. It will p
romote the further commercialization of PEHs.\n\nhttps://indico.mpi-magdeb
urg.mpg.de/event/7/contributions/197/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/197/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Data-driven reduced-order modeling from noisy measurements: new re
sults and future perspectives
DTSTART;VALUE=DATE-TIME:20200729T173000Z
DTEND;VALUE=DATE-TIME:20200729T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-195@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Ion Victor Gosea (MPI Magdeburg)\nThe scope of this
contribution is to present some recent results on how interpolation-based
data-driven methods such as\n\n1. The Loewner framework [Mayo/Antoulas '07
]\;\n2. The AAA algorithm [Nakatsukasa/Sete/Trefethen '18]\;\n\ncan handle
noisy data sets. More precisely\, it will be assumed that the input-outpu
t measurements used in these methods\, i.e.\, transfer function evaluation
s\, are corrupted by additive Gaussian noise.\n\nThe notion of "sensitivit
y to noise" is introduced and it is used to understand how the location of
measurement points affects the "quality" of reduced-order models. For exa
mple\, models that have poles with high sensitivity are hence deemed prohi
bited since even small perturbations could cause an unwanted behavior (suc
h as instability). Moreover\, we show how different data splitting techniq
ues can influence the sensitivity values. This is a crucial step in the Lo
ewner framework\; we present some illustrative examples that include the e
ffects of splitting the data in the "wrong" or in the "right" way.\n\nFina
lly\, some perspectives for the future: we would like to employ statistics
and machine learning techniques in order to avoid "overfitting". More pre
cisely\, it is said that a model that has learned the noise instead of the
true signal is considered an "overfit" because it fits the given noisy da
taset but has a poor fit with other new datasets. We present some possible
ways to avoid "overfitting" for the methods under consideration.\n\nhttps
://indico.mpi-magdeburg.mpg.de/event/7/contributions/195/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/195/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Data-Driven Learning of Reduced-Order Dynamics for a Parametrized
Shallow Water Equation
DTSTART;VALUE=DATE-TIME:20200730T110000Z
DTEND;VALUE=DATE-TIME:20200730T120000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-186@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Süleyman Yildiz (Institute of Applied Mathematics\,
Middle East Technical University\, Ankara\, Turkey)\nA non-intrusive data
-driven model order reduction method is introduced that learns low-dimensi
onal dynamical models for a parametrized non-traditional shallow water equ
ation (NTSWE). The reduced-order model is learnt by setting an appropriate
least-squares optimization problem in a low-dimen-sional subspace. Comput
ational challenges that particularly arise from the optimization problem\,
such as ill-conditioning are discussed. The non-intrusive model order red
uction framework is extended to a parametric case using the parameter depe
ndency at the level of the partial differential equation. The efficiency o
f the proposed non-intrusive method is illustrated to construct reduced-or
der models for NTSWE and compared with an intrusive method\, proper orthog
onal decomposition with Galerkin projection. Furthermore\, the predictabil
ity of both models outside the range of the training data is discussed.\n\
nhttps://indico.mpi-magdeburg.mpg.de/event/7/contributions/186/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/186/
END:VEVENT
BEGIN:VEVENT
SUMMARY:MUQ-hIPPYlib: A Bayesian Inference Software Framework Integrating
Data with Complex Predictive Models under Uncertainty
DTSTART;VALUE=DATE-TIME:20200727T173000Z
DTEND;VALUE=DATE-TIME:20200727T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-190@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Ki-Tae Kim (University of California\, Merced)\nRece
nt years have seen a massive explosion of datasets across all areas of sci
ence\, engineering\, technology\, medicine\, and the social sciences. The
central questions are: How do we optimally learn from data through the len
s of models? And how do we do so taking into account uncertainty in both d
ata and models? These questions can be mathematically framed as Bayesian i
nverse problems. While powerful and sophisticated approaches have been dev
eloped to tackle these problems\, such methods are often challenging to im
plement and typically require first and second order derivatives that are
not always available in existing computational models. In this paper\, we
present an extensible software framework MUQ-hIPPYlib that overcomes this
hurdle by providing unprecedented access to state-of-the-art algorithms fo
r deterministic and Bayesian inverse problems. MUQ provides a spectrum of
powerful Bayesian inversion models and algorithms\, but expects forward mo
dels to come equipped with gradients/Hessians to permit large-scale soluti
on. hIPPYlib implements powerful large-scale gradient/Hessian-based solver
s in an environment that can automatically generate needed derivatives\, b
ut it lacks full Bayesian capabilities. By integrating these two libraries
\, we created a robust\, scalable\, and efficient software framework that
realizes the benefits of each to tackle complex large-scale Bayesian inver
se problems across a broad spectrum of scientific and engineering areas.\n
\nhttps://indico.mpi-magdeburg.mpg.de/event/7/contributions/190/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/190/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Prediction-Based Nature-Inspired Dynamic Optimization
DTSTART;VALUE=DATE-TIME:20200729T173000Z
DTEND;VALUE=DATE-TIME:20200729T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-189@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Almuth Meier (SCHOTT AG)\nThe poster will give insig
hts into my PhD research. I combine time-series prediction and heuristic o
ptimization algorithms to cope with time-varying optimization problems. A
frequent task in dynamic optimization is to track the moving optimum as ac
curately as possible. Originally designed for static optimization\, nature
-inspired algorithms on dynamic problems suffer from premature convergence
. To circumvent this different approaches have been developed\, prediction
is one among others. The trajectory of solutions found during the optimiz
ation process is interpreted as representation of the optimum dynamics. Wi
th time-series prediction techniques that are learned online\, for this tr
ajectory the next step is predicted which in turn is employed to lead the
optimizer's search in direction of the predicted optimum. By this means\,
a faster convergence and tracking accuracy might be achievable.\n\nIn my t
hesis\, I investigate different neural network architectures as prediction
models\, and propose strategies to utilize the prediction in nature-inspi
red optimization algorithms (evolution strategy\, particle swarm optimizat
ion). Furthermore\, I suggest to adapt the optimizer's operators based on
the predictive uncertainty in order to prevent the optimizer from being mi
sled by a poor prediction.\n\nhttps://indico.mpi-magdeburg.mpg.de/event/7/
contributions/189/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/189/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Learning age-related chronic disease progression from cognitive me
asurements
DTSTART;VALUE=DATE-TIME:20200727T173000Z
DTEND;VALUE=DATE-TIME:20200727T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-169@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Cindy Catherine Orozco Bohorquez (Stanford Universit
y)\nCognitive impairment is one of the most prominent symptoms of age-rela
ted diseases such as Alzhei-mer’s disease or Lewy body disease. Therefor
e\, it is not surprising that cognitive impairment is one of the variables
that is usually measured in longitudinal studies of Alzheimer’s disease
. However\, if we look naively at the progression of cognitive impairment
in a patient\, we cannot obtain enough information of the progression of A
lzheimer’s disease in them. The reason of this mismatch is that cognitiv
e impairment is an overlapping symptom caused by multiple chronic diseases
and modulated by intrinsic and extrinsic variables.\n\nEach age-related c
hronic disease\, such as Alzheimer’s disease\, is characterized by a set
of biological processes that can be measured by biomarkers. In recent ye
ars\, multiple machine learning models have been proposed to predict cogni
tive impairment given the measurements of biomarkers of different chronic
diseases. Nevertheless\, measuring biomarkers for a large cohort in a long
itudinal study is more complicated and more expensive than measuring cogni
tive impairment. This results in sparser biomarkers measurements for each
patient. Therefore\, there is the need for a model that reconstructs the b
iomarker progression of different chronic diseases from sparse measurement
s of biomarkers and the progression of cognitive measurements.\n\nOur proj
ect looks for an interpretable and simple model\, that can reconstruct the
progression of different chronic diseases leveraging the mechanistic know
ledge that is available in the literature.\n\nhttps://indico.mpi-magdeburg
.mpg.de/event/7/contributions/169/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/169/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reduced order modelling for data assimilation in parametrized opti
mal control framework
DTSTART;VALUE=DATE-TIME:20200729T173000Z
DTEND;VALUE=DATE-TIME:20200729T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-192@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Maria Strazzullo (SISSA\, mathLab)\nModelling data a
ssimilation allows to fill the gap between numerical simulations and exper
imental data. Optimal control problems governed by parametrized partial di
fferential equations is suited for this kind of application\, where you wa
nt to track problem solutions towards known quantities\, given by data col
lections or previous knowledge. Still\, the computational effort increases
when one has to deal with nonlinear and/or time-dependent governing equat
ions.\nReduced order methods are an effective approach to solve data assim
ilation problems in a reliable and faster way. We apply the POD-Galerkin m
ethodology in environmental marine sciences where different parameters des
cribe several physical configurations.\nWe present two numerical experimen
ts: a boundary control for riverbed current represented by time-dependent
Stokes equations\, and a nonlinear time-dependent tracking problem for vel
ocity-height solutions of shallow water equations.\n\nhttps://indico.mpi-m
agdeburg.mpg.de/event/7/contributions/192/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/192/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Deep Kernel approaches with a Neural-Network-like structure
DTSTART;VALUE=DATE-TIME:20200730T110000Z
DTEND;VALUE=DATE-TIME:20200730T120000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-157@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Tizian Wenzel (University of Stuttgart)\nKernel meth
ods provide a mathematically rigorous way of learning\, however they usual
ly lack efficiency on large amounts of data due to a bad scaling in the nu
mber of data points. Furthermore\, they are flat models\, in the sense tha
t they consist only of one linear combination of non-linear functions. Ano
ther drawback is that they do not allow for end-to-end learning\, since th
e model learning is decoupled from the data representation learning. In co
ntrast\, Neural Network techniques are able to make use of such large amou
nts of data and computational resources and combine the representation lea
rning with the model learning.\n\nBased on a recent Representer Theorem fo
r Deep Kernel learning [1]\, we examine different setups and optimization
strategies for Deep Kernels including some theoretical analysis. We show t
hat - even with simple kernel functions - the Deep Kernel approach leads t
o setups similar to Neural Networks but with optimizable activation functi
ons. A combination of optimization and regularization approaches from both
Kernel methods and Deep Learning methods\, yields to improved accuracy in
comparison to flat kernel models. Furthermore\, the proposed approach eas
ily scales to large amounts of training data in high dimension which is im
portant from the application point of view. Preliminary results on a fluid
dynamics application (with a dataset with up to 17 million data points in
30 dimensions show favorable results compared to standard Deep Learning m
ethods [2].\n\n[1] Bohn\, Bastian\, Christian Rieger\, and Michael Griebel
. "A Representer Theorem for Deep Kernel Learning." Journal of Machine Lea
rning Research 20.64 (2019): 1-32.\n[2] T. Wenzel\, G. Santin\, B. Haasdon
k: "Deep Kernel Networks: Analysis and Comparison"\, Preprint\, University
of Stuttgart\, in preparation.\n\nhttps://indico.mpi-magdeburg.mpg.de/eve
nt/7/contributions/157/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/157/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Modulus-based iterative methods for constrained $\\ell_p$-$\\ell_q
$ minimization
DTSTART;VALUE=DATE-TIME:20200727T173000Z
DTEND;VALUE=DATE-TIME:20200727T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-196@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Mirjeta Pasha (Arizona State University)\nThe need t
o solve discrete ill-posed problems arises in many areas of science and en
gineering. Solutions of these problems\, if they exist\, are very sensitiv
e to perturbations in available data. Regularization replaces the original
problem by a nearby regularized problem\, whose solution is less sensitiv
e to the error in the data. The \nregularized problem contains a fidelity
term and a regularization term. Recently\, the use of a $p$-norm to measu
re the fidelity term and a $q$-norm to measure the regularization term has
received considerable attention. The balance between these terms is deter
mined by a regularization parameter. In many applications\, such as in ima
ge restoration\, the desired solution is known to live in a convex set\, s
uch as the nonnegative orthant. It is natural to require the computed solu
tion of the regularized problem to satisfy the same constraint(s). This pa
per shows that this procedure induces a regularization method and describe
s a modulus-based iterative method for computing a constrained approximate
solution of a smoothed version of the regularized problem. Convergence of
the iterative method is shown\, and numerical examples that illustrate t
he performance of the proposed method are presented.\n\nhttps://indico.mpi
-magdeburg.mpg.de/event/7/contributions/196/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/196/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fusing Online Gaussian Process-Based Learning and Control for Scan
ning Quantum Dot Microscopy
DTSTART;VALUE=DATE-TIME:20200729T173000Z
DTEND;VALUE=DATE-TIME:20200729T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-194@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Maik Pfefferkorn (Otto-von-Guericke University Magde
burg)\nScanning quantum dot microscopy is a technique for imaging electros
tatic surface potentials with atomic resolution. To this end it uses a sen
sor molecule\, the so-called quantum dot (QD)\, which is bonded to the tip
of a frequency modulated non-contact atomic force microscope. The QD is m
oved in the vicinity of the surface atoms so that it experiences the surfa
ce potential. By superimposing an external potential using a tip-surface b
ias voltage V_b\, the QD's potential is modulated to reach critical values
at which the QD changes its charge state. In consequence to these chargin
g events\, the tuning fork's oscillation frequency $f$ changes abruptly\,
making the charging events appear as dips in the so-called spectrum $\\Del
ta f(V_b)$\, characterized by the positions $V^{\\mp}$ of their respective
minimum points. These dip positions $V^{\\mp}$ are used for reconstructin
g the surface potential image.\n\nWhile scanning the sample in a raster pa
ttern\, $V^{\\mp}$ change with the position of the dip in consequence of t
he sample topography and its electrical properties. To efficiently and rel
iably track $V^{\\mp}$ we have employed a two-degree-of-freedom control pa
radigm within which a Gaussian process and an extremum seeking controller
are used. The Gaussian process is employed in the feedforward part to comp
ute a prediction of $V^{\\mp}$ for the next line based on the data of prev
ious lines. This prediction is thereafter applied pixel by pixel as initia
l point to the extremum seeking controller\, which is used in the feedback
part to correct deviations between the prediction and the true value. Obt
aining an accurate prediction is hereby critical for correct operation as
the extremum seeking controller is only capable of tracking $V^{\\mp}$ as
long as the current value $V_b$ is within the dip. For reducing the comput
ation time in order to make the controller suitable for utilization in pra
ctice\, we have implemented and tested different approximation approaches
for sparse GP implementation.\n\nIn simulative testings\, we have shown th
at using the proposed two-degree-of-freedom control para-digm results in s
horter scan times while achieving a high image quality when compared to fe
edback control only. The most promising approximation approach for sparse
GP implementation regarding scan time and image quality has been found to
be the fully independent training conditional approximation. We have furth
er shown that its computation is sufficiently low for usability in practic
e.\n\nhttps://indico.mpi-magdeburg.mpg.de/event/7/contributions/194/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/194/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chance-constrained optimal control of hyperbolic supply systems
DTSTART;VALUE=DATE-TIME:20200730T110000Z
DTEND;VALUE=DATE-TIME:20200730T120000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-198@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Kerstin Lux (Technical University of Munich)\nWe are
concerned with optimal control strategies subject to uncertain demands. I
n many real-world situations\, taking uncertainty into account gains in im
portance. Supply chain management and the energy transition are just two e
xamples where control strategies coping with uncertainties are of high pra
ctical importance. A compensation of deviations from the actual demand mig
ht be very costly and should be avoided. To address this problem\, we cont
rol the inflow in the hyperbolic supply system at a given time to optimall
y meet an uncertain demand stream. To enhance supply reliability\, we requ
ire demand satisfaction at a prescribed probability level\, mathematically
formulated in terms of a chance constraint. The stochastic optimal contro
l framework has been set up in [LGK19]. The hyperbolic supply system is mo
deled by hyperbolic balance laws and the Ornstein-Uhlenbeck process repres
ents the uncertain demand stream.\n\nIn future work\, we would like to ext
end the setting to include uncertainty not only in the demand but also wit
hin the model of the supply system\, where parameters shall be learned fro
m data.\n\nAcknowledgment: The authors are grateful for the support of th
e German Research Foundation (DFG) within the project ``Novel models and c
ontrol for networked pro\\-blems: from discrete event to continuous dynami
cs'' (GO1920/4-1).\n\n[LGK19] Lux\, K.\, Göttlich\, S.\, and Korn\, R. ``
Optimal control of electricity input given an uncertain demand.''\, MMOR\,
2019.\n\nhttps://indico.mpi-magdeburg.mpg.de/event/7/contributions/198/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/198/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stochastic Grey-box Model of the Flow-Front Dynamics
DTSTART;VALUE=DATE-TIME:20200730T110000Z
DTEND;VALUE=DATE-TIME:20200730T120000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-200@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Rishi Relan (Siemens Energy\, Technical University o
f Denmark\, BML Munjal University)\nWith the continuously increasing size
of the wind turbine blades\, the complexity of the blade casting process a
nd the risk of failures has also increased. The vacuum-assisted resin tran
sfer moulding (VATRM) production process at the Siemens Gamesa Renewable E
nergy facility in Aalborg\, Denmark\, does not permit the visual inspectio
n of the process. Hence a sensor system (possibly virtual) for process con
trol and monitoring is highly prized. Therefore\, in this poster\, a simp
le methodology to identify a low-dimensional stochastic grey-box spatiotem
poral model of the flow-front dynamics inside the vacuum assisted resin tr
ansfer moulding process is described. A numerical case-study is presented
demonstrating the effectiveness of the proposed methodology.\n\nhttps://in
dico.mpi-magdeburg.mpg.de/event/7/contributions/200/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/200/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Data-driven computational continuum mechanics
DTSTART;VALUE=DATE-TIME:20200730T110000Z
DTEND;VALUE=DATE-TIME:20200730T120000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-202@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Vu Chau (University of Luxembourg )\nMy research's t
opic focuses on developing and investigating computational data-driven met
hods in order to model the material laws from observed data. The methodolo
gy is expected to deliver the governing mathematical model of the observed
problem in the form of a set of symbolic equations that potentially enabl
e new discoveries in data-rich fields of continuous physical problems. Art
ificial neural networks (ANN) have been proposed as an efficient data-driv
en method for constitutive modelling\, accepting either synthetic data sol
utions or experimental datasets. Sparse regression has the potential to id
entify relationships between field quantities directly from data in the fo
rm of symbolic expressions. Depending on the richness of the given data (f
unction values vs. gradients\, densely vs. sparsely sampled) specific tech
niques are required to obtain accurate numerical evaluations of spatial an
d temporal derivatives from sparse data representing smooth or non-smooth
states\; e.g. via hierarchical multi-level gradient estimation\, Gaussian
smoothing or gradient capturing techniques. A machine learning prototype i
s implemented using the FEniCS framework coupled with a trained neural net
work on the basis of PyTorch.\n\nhttps://indico.mpi-magdeburg.mpg.de/event
/7/contributions/202/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/202/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quantifying incompressible two-phase flow fields from the interfac
e movement using physics-informed neural networks
DTSTART;VALUE=DATE-TIME:20200730T110000Z
DTEND;VALUE=DATE-TIME:20200730T120000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-201@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Aaron Buhendwa (Technical University Munich\, Chair
of Aerodynamics and Fluid mechanics)\nPhysics-informed neural networks are
applied to incompressible two-phase flow problems. We investigate the for
ward problem\, where the governing equations are solved from initial and b
oundary conditions\, as well as the inverse problem\, where continuous vel
ocity and pressure fields are inferred from data on the interface positio
n scattered across time. We employ a volume of fluid approach\, i.e. the a
uxiliary variable here is the volume fraction of the fluids within each ph
ase. For the forward problem\, we solve a two-phase Couette and Poiseuill
e flow. As for the inverse problem\, three classical test cases in two-pha
se modeling are investigated. In particular\, a drop in a shear flow\, an
oscillating drop and a rising bubble is studied. The data of the interface
position over time is generated with a valitated CFD solver. The inferred
velocity and pressure fields are then compared to the CFD solution. An ef
fective way to distribute the spatial training points to fit the interface
\, i.e. the volume fraction field\, and the residual points is presented.
Furthermore\, we show that the weighting of the losses that are associated
with the residua of the partial differential equations is crucial for the
training process. The benefit of using adaptive activation functions is e
valuated for both the forward and inverse problem.\n\nhttps://indico.mpi-m
agdeburg.mpg.de/event/7/contributions/201/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/201/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A function space random feature model for PDE solution maps
DTSTART;VALUE=DATE-TIME:20200727T173000Z
DTEND;VALUE=DATE-TIME:20200727T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-204@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Nicholas H. Nelsen (Caltech)\nWe propose a supervise
d learning methodology for use of the random feature model as a data-drive
n surrogate for operators mapping between spaces of functions. Although ou
r methodology is quite general\, we consider operators defined by partial
differential equations (PDEs)\; here\, the inputs and outputs are themselv
es functions\, with the input parameters being functions required to speci
fy a well-posed problem and the outputs being solutions of the problem. Up
on discretization\, the model inherits several desirable attributes from t
his function space viewpoint\, including mesh-invariant approximation erro
r and the capability to be trained at one mesh resolution and then deploye
d at different mesh resolutions. We demonstrate the random feature model's
ability to cheaply and accurately approximate the nonlinear parameter-to-
solution maps of prototypical PDEs arising in physical science and enginee
ring applications\, which suggests the applicability of the method as a su
rrogate for expensive full-order forward models arising in many-query prob
lems.\n\nhttps://indico.mpi-magdeburg.mpg.de/event/7/contributions/204/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/204/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A data-driven physics-informed finite-volume scheme for nonclassic
al undercompressive shocks
DTSTART;VALUE=DATE-TIME:20200730T110000Z
DTEND;VALUE=DATE-TIME:20200730T120000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-207@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Deniz A Bezgin (Technical University of Munich)\nIn
my PhD work\, I am combining established numerical methods with machine le
arning techniques to build adaptive and highly accurate numerical schemes
for fluid mechanics. Currently\, I am interested in how neural networks ca
n enhance the flux reconstruction process in finite-volume schemes. Most r
ecently\, I have submitted the journal paper “A data-driven physics-info
rmed finite-volume scheme for nonclassical undercompressive shocks” to t
he Journal of Computational Physics. The abstract reads as follows:\n„We
propose a data-driven physics informed finite volume scheme for the appro
ximation of small-scale dependent shocks. Nonlinear hyperbolic conservatio
n laws with non-convex fluxes allow nonclassical shock wave solutions. In
this work\, we consider the cubic scalar conservation law as a representat
ive of such systems. As standard numerical schemes fail to approximate non
classical shocks\, schemes with controlled dissipation and schemes with we
ll-controlled dissipation have been introduced by LeFloch and Mohammadian
and by Ernest and coworkers\, respectively. Emphasis has been placed on ma
tching the truncation error of the numerical scheme with physically releva
nt small-scale mechanisms. However\, aforementioned schemes can introduce
oscillations as well as excessive dissipation around shocks. In our approa
ch\, a convolutional neural network is used for an adaptive nonlinear flux
reconstruction. Based on the local flow field\, the network combines loca
l interpolation polynomials with a regularization term to form the numeric
al flux. This allows to modify the discretization error by nonlinear terms
. Via a supervised learning task\, the model is trained to predict the tim
e evolution of exact solutions to Riemann problems using the method of lin
es. The model is physics informed as it respects the underlying conservati
on law. Numerical experiments for the cubic scalar conservation law show t
hat the resulting method is able to approximate nonclassical shocks very w
ell. The adaptive reconstruction surpresses oscillations and enables sharp
shock capturing. Generalization to unseen shock configurations and smooth
intial value problems is robust and shows very good results.“ \nIn afor
ementioned work\, the machine learning part is limited to the selection of
local interpolation polynomials and combining them with regularization te
rms. This is done in order to guarantee a physically consistent numerical
scheme. I am very much interested in how to relax these restrictions on th
e machine learning part while maintaining physical consistency in a numeri
cal method. Therefore\, in my poster I will present details on the data-dr
iven scheme for undercompressive nonclassical shocks and possible extensio
ns as to how the machine learning part can be further extended.\n\nhttps:/
/indico.mpi-magdeburg.mpg.de/event/7/contributions/207/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/207/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Model Reduction for Advection Dominated Problems
DTSTART;VALUE=DATE-TIME:20200730T110000Z
DTEND;VALUE=DATE-TIME:20200730T120000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-206@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Davide Torlo (University of Zurich)\nModel order red
uction for advection dominated problems has always been not effective due
to the slow decay of the Kolmogorov $N$-width of the problems. Even very s
imple problems\, such as linear transport equations of sharp gradients\, s
how already this behavior. This difficulty can be overcome with different
techniques. What we propose is to change the original solution manifold th
anks to a geometrical transformation that aligns the advected features of
the different solutions and that leads to an Arbitrary Lagrangian Eulerian
formulation.\nIn order to be able to use this formulation\, we need to kn
ow the so-called mesh velocity. In this context\, the map is chosen accord
ing to parameter and time and can be generated with some expensive detecti
on and optimization algorithms. To effectively use it in the online phase
of the model order reduction technique a regression map must be used. To d
o so\, we compare different regression maps (polynomials and deep learning
maps). The results for some examples in 1D are shown. \nMore details on
https://arxiv.org/abs/2003.13735\n\nhttps://indico.mpi-magdeburg.mpg.de/e
vent/7/contributions/206/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/206/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Data-based Approach for Fault Diagnosis of Hydropower Rotors
DTSTART;VALUE=DATE-TIME:20200730T110000Z
DTEND;VALUE=DATE-TIME:20200730T120000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-208@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Christian Sperber (Voith Hydro Holding GmbH & Co. KG
)\nThe poster presents a novel approach to diagnose rotordynamic faults li
ke unbalance and coupling misalignment from measured vibration. For that p
urpose\, a large database of virtual hydropower rotors and their vibration
has been calculated. The goal is to create a data-driven diagnosis system
from this database\, that will be applicable to a variety of real hydropo
wer rotors. In a first step\, a gradient boosting regression algorithm has
been applied to the database with some preprocessing and showed promising
results that now shall be improved in accuracy.\n\nhttps://indico.mpi-mag
deburg.mpg.de/event/7/contributions/208/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/208/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Insights into squealing disk brakes through explainable machine le
arning for time series data
DTSTART;VALUE=DATE-TIME:20200730T110000Z
DTEND;VALUE=DATE-TIME:20200730T120000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-210@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Merten Stender (Hamburg University of Technology)\nF
riction brakes can exhibit high-intensity vibrations in the frequency rang
e above 1 kHz\, which is typically known as squeal. Those vibrations are s
elf-excited due to the friction-interface between brake pads and disk. Dec
ades of research have been spent on modelling this phenomenon\, but even t
oday predictive modelling is out of reach. The root causes\, amongst other
s\, are considered to be the multi-scale temporal effects\, multi-physic i
nteractions involving mechanics\, thermodynamics and chemistry\, unknown s
ystem parameters and emergent behaviour. Continuing recent works\, we pres
ent a machine learning approach to predict the dynamic instability from mu
ltiple complex loading conditions using recurrent neural networks and a la
rge experimental database. In order to generate new designs that are less
prone to self-excited vibrations\, the trained networks are exposed to mod
el-agnostic explainers\, that can disaggregate the complex nonlinear relat
ions that were learned during the training phase. Importance values are as
signed to loading sequences and are visualized by colour mappings. The val
idated models are virtual twins for the actual brake system and can serve
as a reduce-order model. Furthermore\, classical analytical models are com
pared and updated using the virtual twins for generating low-dimensional r
epresentations of complex dynamical systems.\n\nhttps://indico.mpi-magdebu
rg.mpg.de/event/7/contributions/210/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/210/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weak SINDy: Galerkin-Based Data-Driven Model Selection
DTSTART;VALUE=DATE-TIME:20200727T173000Z
DTEND;VALUE=DATE-TIME:20200727T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-212@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Daniel Messenger (University of Colorado Boulder)\nW
e present a weak formulation and discretization of the system discovery pr
oblem from noisy measurement data. This method of learning differential eq
uations from data replaces point-wise derivative approximations with local
integration and improves on the standard SINDy algorithm by orders of mag
nitude. Linear transformations associated with local integration are used
to construct covariance matrices which enforce discovery of parsimonious b
est-fit models by accurately scaling the error in the residuals during seq
uentially-thresholded generalized least squares. In the absence of noise\,
this so-called Weak SINDy framework (WSINDy) is capable of recovering the
correct nonlinearities from synthetic data with error in the recovered co
efficients falling below the tolerance of the data simulation scheme. As d
emonstrated by adding white noise directly to the state variables\, WSINDy
also naturally accounts for measurement noise\, with errors in the recove
red coefficients scaling proportionally to the signal-to-noise ratio\, whi
le significantly reducing the required number of data points and the size
of linear systems involved. Altogether\, WSINDy combines the ease of imple
mentation of the SINDy algorithm with the natural noise-reduction of integ
ration to arrive at a more robust and user-friendly method of sparse recov
ery that correctly identifies systems in both small-noise and large-noise
regimes. Examples include nonlinear ODEs (Van der Pol Oscillator\, Lorenz
system) and PDEs (Allen-Cahn\, Kuramato-Sivashinsky\, Reaction-Diffusion s
ystems) with sharp transitions and/or chaotic behavior.\n\nhttps://indico.
mpi-magdeburg.mpg.de/event/7/contributions/212/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/212/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Data-driven metamodelling in Global Sensitivity Analysis
DTSTART;VALUE=DATE-TIME:20200729T173000Z
DTEND;VALUE=DATE-TIME:20200729T183000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-213@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Panagiotis Demis (Department of Chemical and Process
Engineering\, University of Surrey)\nComputer simulations of natural and
physical systems are subject to various sources of uncertainty necessitati
ng the facilitation of uncertainty quantification and sensitivity analysis
methods in the development of mathematical models. As complexity of mathe
matical models grows\, non-intrusive methods draw the attention for identi
fication and characterisation of uncertainties in model outputs. In this s
etting\, Global Sensitivity Analysis (GSA) enables a holistic approach to
apportioning output uncertainty to uncertain model inputs. The advantage o
f GSA over previous local sensitivity analysis methods is the computation
of sensitivity indices for wider classes of mathematical models considerin
g nonlinear statistical and structural dependencies among inputs and outpu
ts [1]. However\, GSA requires the estimation of conditional variances bas
ed on Monte Carlo simulations\, which might be computationally prohibitive
for physical models of high complexity. Addressing this issue\, metamodel
-based GSA methods have been developed to utilise data-driven models as su
rrogate response surfaces that accelerate GSA [2]. The authors aim to inco
rporate recent advances in machine learning for system identification and
model reduction with implications for the computational efficiency of GSA.
\n\nReferences:\n1. Iooss\, B. and Lemaître\, P. (2014) ‘A review on gl
obal sensitivity analysis methods’\, *Uncertainty management in Simulati
on-Optimization of Complex Systems: Algorithms and Applications*\, 30\, p.
23. doi: 10.1007/978-1-4899-7547-8_5.\n2. Gratiet\, L. Le\, Marelli\, S.
and Sudret\, B. (2016) ‘Metamodel-Based Sensitivity Analysis: Polynomial
Chaos Expansions and Gaussian Processes’\, in Ghanem\, R.\, Higdon\, D.
\, and Owhadi\, H. (eds) *Handbook of Uncertainty Quantification*. Cham: S
pringer International Publishing\, pp. 1–37. doi: 10.1007/978-3-319-1125
9-6_38-1.\n\nhttps://indico.mpi-magdeburg.mpg.de/event/7/contributions/213
/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/213/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Can machine learning methods be used to create parametrized reduce
d models of vibro-acoustic systems?
DTSTART;VALUE=DATE-TIME:20200730T110000Z
DTEND;VALUE=DATE-TIME:20200730T120000Z
DTSTAMP;VALUE=DATE-TIME:20210803T142912Z
UID:indico-contribution-7-215@indico.mpi-magdeburg.mpg.de
DESCRIPTION:Speakers: Quirin Aumann (Technical University of Munich\, Chai
r of Structural Mechanics)\nThe optimization of vibro-acoustic systems in
terms of vibration or sound radiation requires many system evaluations for
varying parameters. Often\, material or geometric uncertainties have to b
e considered. Vibro-acoustic systems are typically large and numerically e
xpensive to solve\, so it is desirable to use an efficient parametrized su
rrogate model for optimization tasks. Classic reduced order modelling has
already been used to create parametrized reduced models of vibro-acoustic
systems (Aumann et al. 2019\; van Ophem et al. 2019). In this contribution
\, we want to investigate the potential of using machine learning techniqu
es\, such as neural networks or regression models to create parametrized
surrogate models for vibro-acoustic systems.\n\nSwischuk et al. (2019) cre
ated parametrized surrogate models for a structural system combining reduc
ed order modelling and machine learning methods. They used proper orthogon
al decomposition (POD) for non-linear systems in the time domain to genera
te the POD coefficients and trained their surrogate model with a neural ne
twork and different regression methods to map parameter sets to POD coeffi
cients. Their resulting surrogate model is used for real-time structural d
amage evaluation. We want to pursue a similar approach for vibro-acoustic
systems in the frequency domain. Using a classic model order reduction met
hod\, we extract the dominant modes of systems with given parameter sets a
nd use them to train a surrogate model. The model shall be trained to find
the proper poles of the reduced system given an unknown set of parameters
. Using the poles\, a reduced order model for this parameter set can be cr
eated and evaluated efficiently. Its response can also be transformed to o
btain the full system’s response and can be used for optimization tasks.
\n\nSuch a surrogate model can be used\, for example\, to optimize the rad
iation characteristics of a violin\, which heavily depends on the thicknes
s of its corpus and the used materials. Another application is system iden
tification. The surrogate model can be trained to map obstacle locations i
n an acoustic cavity to its response to a defined excitation. In an invert
ed process\, the trained model can then test an actual response resulting
from an obstacle against possible obstacle locations to find its actual po
sition. \n\nReferences:\nAumann\, Q.\; Miksch\, M.\; Müller\, G. (2019):
Parametric model order reduction for acoustic metamaterials based on local
thickness variations. In *J. Phys.: Conf. Ser.* 1264\, p. 12014. DOI: 10.
1088/1742-6596/1264/1/012014.\nSwischuk\, Renee\; Mainini\, Laura\; Pehers
torfer\, Benjamin\; Willcox\, Karen (2019): Projection-based model reducti
on: Formulations for physics-based machine learning. In *Computers & Fluid
s* 179\, pp. 704–717. DOI: 10.1016/j.compfluid.2018.07.021.\nvan Ophem\,
S.\; Deckers\, E.\; Desmet\, W. (2019): Parametric model order reduction
without a priori sampling for low rank changes in vibro-acoustic systems.
In *Mechanical Systems and Signal Processing* 130\, pp. 597–609. DOI: 10
.1016/j.ymssp.2019.05.035.\n\nhttps://indico.mpi-magdeburg.mpg.de/event/7/
contributions/215/
LOCATION:
URL:https://indico.mpi-magdeburg.mpg.de/event/7/contributions/215/
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