UQSay #63

2–3 PM — Stefania Fresca (MOX, Dept. of Mathematics, Politecnico di Milano)

Deep learning-based reduced order models for the real-time approximation of parametrized PDEs

Conventional reduced order models (ROMs) anchored to the assumption of modal linear superimposition, such as proper orthogonal decomposition (POD), may reveal inefficient when dealing with nonlinear time-dependent parametrized PDEs, especially for problems featuring coherent structures propagating over time. To enhance ROM efficiency, we propose a nonlinear approach to set ROMs by exploiting deep learning (DL) algorithms, such as convolutional neural networks. In the resulting DL-ROM, both the nonlinear trial manifold and the nonlinear reduced dynamics are learned in a non-intrusive way by relying on DL algorithms trained on a set of full order model (FOM) snapshots, obtained for different parameter values. Performing then a former dimensionality reduction on FOM snapshots through POD enables, when dealing with large-scale FOMs, to speedup training times, and decrease the network complexity, substantially. Accuracy and efficiency of the DL-ROM technique are assessed on different parametrized PDE problems in cardiac electrophysiology, computational mechanics and fluid dynamics, possibly accounting for fluid-structure interaction (FSI) effects, where new queries to the DL-ROM can be computed in real-time. Moreover, numerical results obtained by the application of DL-ROMs to the solution of an industrial application, i.e. the approximation of the structural or the electromechanical behaviour of Micro-Electro-Mechanical Systems (MEMS), will be shown.

References:

1. G. Gobat, S. Fresca, A. Manzoni, A. Frangi, “Reduced order modelling of nonlinear vibrating multiphysics microstructures with deep learning-based approaches”, Sensors, vol. 23, no. 6, pp. 3001, 2023 .
2. S. Fresca, G. Gobat, P. Fedeli, A. Frangi, A. Manzoni, “Deep learning-based reduced order models for the real-time simulation of the nonlinear dynamics of microstructures”, International Journal for Numerical Methods in Engineering, vol. 123, no. 20, pp. 4749-4777, 2022 .
3. S. Fresca, A. Manzoni, “POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition”, Computer Methods in Applied Mechanics and Engineering, vol. 388, pp. 114181, 2022 .
4. S. Fresca, A. Manzoni, L. Dede’, A. Quarteroni, “POD-enhanced deep learning-based reduced order models for the real-time simulation of cardiac electrophysiology in the left atrium”, Frontiers in Physiology, vol. 12, pp. 1431, 2021 .
5. S. Fresca, A. Manzoni, “Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models”, Fluids, vol. 6, no. 7, pp. 259, 2021 .
6. S. Fresca, A. Manzoni, L. Dede’, “A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs”, Journal of Scientific Computing, vol. 87, no. 2, pp. 1-36, 2021 .

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Emmanuel Vazquez (L2S).

Coordinators: Julien Bect (L2S) & Sidonie Lefebvre (ONERA)

Practical details: the seminar will be held online using Microsoft Teams.

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