Prof. Siddhartha Mishra

Title: Deep Learning and Computation of PDEs

Abstract: In this talk, we will review some recent results on computing PDEs with deep neural networks. The focus will be on the design of neural networks as fast and efficient surrogates for PDEs. We will start with parametric PDEs and talk about novel modifications that enable standard deep neural networks to provide efficient PDE surrogates and apply them for prediction, uncertainty quantification and PDE constrained optimization. We will also cover very recent results on operator regression using novel architectures such as DeepOnets and Fourier Neural Operators, and their application to PDEs.