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Séminaire du LJLL - 12 11 2021 14h00 : S. Mishra
Vendredi 12 novembre 2021 — 14h00
Exposé à distance avec retransmission par Zoom en temps réel
Siddharta Mishra (Ecole Polytechnique Fédérale de Zurich)
Deep learning and computations of high-dimensional PDEs
Résumé
Partial Differential Equations (PDEs) with very high-dimensional state and/or parameter spaces arise in a wide variety of contexts ranging from computational chemistry and finance to many-query problems in various areas of science and engineering. In this talk, we will survey recent results on the use of deep neural networks in computing these PDEs. We will focus on two different aspects i.e., the use of supervised deep learning, in the form of both standard deep neural networks as well as recently proposed Operator learning frameworks, for efficient approximation of many-query PDEs and the use of unsupervised learning in the form of physics informed neural-networks (PINNs) for the computation of forward and inverse problems for PDEs with high-dimensional state spaces.