MaLGa Seminar: Andrea Manzoni "Deep learning-based reduced order models for the real-time numerical approximation of PDEs", January 24th 15:00 room 705/Youtube
Matteo Santacesaria
Apologies for multiple posting.
We are pleased to announce the next MaLGa Seminar Series
- Analysis and Learning.
This event is part of the Ellis Genoa activities.
Speaker: Andrea Manzoni
Affiliation: MOX, Politecnico di Milano
Date: Monday, January 24th, 2022
Time: 15:00 p.m.
Location: room 705, via Dodecaneso 35, Genova, IT
Live streaming will be available at https://www.youtube.com/channel/UCU8upIJcI-BFUdFeYUwjJfg/featured
Title: Deep learning-based reduced order models for the
real-time numerical approximation of PDEs
Abstract: Conventional reduced order modeling techniques such as
the reduced basis method (relying, e.g., on proper orthogonal
decomposition (POD)) may incur in severe limitations when
dealing with nonlinear time-dependent parametrized PDEs, as
these are strongly anchored to the assumption of modal linear
superimposition. To overcome them, we have recently proposed a
new, nonlinear approach to set reduced order models (ROMs) by
exploiting deep learning (DL) algorithms. In the resulting
DL-ROMs, both the nonlinear trial manifold and the nonlinear
reduced dynamics are learned in a non-intrusive way, by relying
on deep (e.g., feedforward, convolutional, autoencoder) neural
networks; these latter are trained on a set of full order model
solutions obtained for different parameter values. Although
extremely efficient at testing time, when evaluating the PDE
solution for any new testing-parameter instance, DL-ROMs might
still require an expensive training stage, because of the
extremely large number of network parameters to be estimated. A
substantial speed up in the training stage of DL-ROMs can be
achieved by (i) performing a prior dimensionality reduction
through POD, and (ii) relying on a multi-fidelity pretraining
stage, where different physical models can be efficiently
combined. The resulting POD-DL-ROM strategy is thus easy to
train, and enables real-time solutions of nonlinear
time-dependent parametrized PDEs. Numerical results dealing with
a variety of problems - such as, e.g., nonlinear
diffusion-reaction, nonlinear elastodynamics, unsteady
Navier-Stokes equations and fluid-structure interaction problems
will show the generality of this approach and its remarkable
computational savings.
Bio: Andrea Manzoni is an associate professor of numerical
analysis at Politecnico of Milan. He is the author of 3 books
and of approximately 60 papers. He got his Ph.D. in Mathematics
from EPFL, Lausanne. He won in 2012 the ECCOMAS Award for the
best PhD thesis in Europe about computational methods in applied
sciences and engineering and the Biannual SIMAI prize (Italian
Society of Applied and Industrial Mathematics) in 2017. His
research interests include the development of reduced-order
modeling techniques for PDEs, PDE-constrained optimization,
uncertainty quantification, computational statistics, and
machine/deep learning.
Matteo Santacesaria
Assistant Professor
MaLGa - Machine Learning Genoa
Center
Department of Mathematics
University of Genoa
Personal
Homepage
Matteo Santacesaria
Apologies for multiple posting.
We are pleased to announce the next MaLGa Seminar Series
- Analysis and Learning.
This event is part of the Ellis Genoa activities.
Speaker: Andrea Manzoni
Affiliation: MOX, Politecnico di Milano
Date: Monday, January 24th, 2022
Time: 15:00 p.m.
Location: room 705, via Dodecaneso 35, Genova, IT
Live streaming will be available at 705DIMA - YouTube
Title: Deep learning-based reduced order models for the
real-time numerical approximation of PDEs
Abstract: Conventional reduced order modeling techniques such as
the reduced basis method (relying, e.g., on proper orthogonal
decomposition (POD)) may incur in severe limitations when
dealing with nonlinear time-dependent parametrized PDEs, as
these are strongly anchored to the assumption of modal linear
superimposition. To overcome them, we have recently proposed a
new, nonlinear approach to set reduced order models (ROMs) by
exploiting deep learning (DL) algorithms. In the resulting
DL-ROMs, both the nonlinear trial manifold and the nonlinear
reduced dynamics are learned in a non-intrusive way, by relying
on deep (e.g., feedforward, convolutional, autoencoder) neural
networks; these latter are trained on a set of full order model
solutions obtained for different parameter values. Although
extremely efficient at testing time, when evaluating the PDE
solution for any new testing-parameter instance, DL-ROMs might
still require an expensive training stage, because of the
extremely large number of network parameters to be estimated. A
substantial speed up in the training stage of DL-ROMs can be
achieved by (i) performing a prior dimensionality reduction
through POD, and (ii) relying on a multi-fidelity pretraining
stage, where different physical models can be efficiently
combined. The resulting POD-DL-ROM strategy is thus easy to
train, and enables real-time solutions of nonlinear
time-dependent parametrized PDEs. Numerical results dealing with
a variety of problems - such as, e.g., nonlinear
diffusion-reaction, nonlinear elastodynamics, unsteady
Navier-Stokes equations and fluid-structure interaction problems
will show the generality of this approach and its remarkable
computational savings.
Bio: Andrea Manzoni is an associate professor of numerical
analysis at Politecnico of Milan. He is the author of 3 books
and of approximately 60 papers. He got his Ph.D. in Mathematics
from EPFL, Lausanne. He won in 2012 the ECCOMAS Award for the
best PhD thesis in Europe about computational methods in applied
sciences and engineering and the Biannual SIMAI prize (Italian
Society of Applied and Industrial Mathematics) in 2017. His
research interests include the development of reduced-order
modeling techniques for PDEs, PDE-constrained optimization,
uncertainty quantification, computational statistics, and
machine/deep learning.