CMAI Colloquium: Deep Learning and Computations of PDEs

Speaker: Dr. Siddhartha Mishra, Department of Mathematics, ETH Zurich 

We present recent results on the use of deep learning techniques in the context of computing different aspects of PDEs. The first part of the talk will be on novel supervised learning algorithms for efficient computation of parametric PDEs with applications to Uncertainty quantification and PDE constrained optimization. The second part of the talk will be focussed on a recently proposed class of unsupervised learning algorithms, Physics Informed Neural Networks (PINNs) and we describe their application to compute solutions for the forward problem for high-dimensional PDE as well as for the data assimilation inverse problems for PDEs.