Webinar: Deep Learning and Computations of High-Dimensional Partial Differential Equations (PDEs)

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. This lecture was on surveying recent results on the use of deep neural networks in computing these high-dimensional PDEs. Focus was on two different aspects: the use of supervised deep learning, in the form of both standard deep neural networks as well as recently proposed DeepOnets, for efficient approximation of many-query PDEs; and the use of physics informed neural-networks (PINNs) for the computation of forward and inverse problems for PDEs with high-dimensional state spaces. The speaker was Professor Siddhartha Mishra, a Professor of Computational Applied Mathematics at ETH Zurich, Switzerland, the Director of Computational Science Zurich, and an associate faculty member at the ETH Artificial Intelligence Center.