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.
This colloquium is part of the Distinguished Lecture Series (DLS) organized by The (Indian) Mathematics Consortium (TMC), and co-hosted by IIT-B and ICTS-TIFR. For more information about this lecture series, and to register, please visit the homepage of the TMC DLS.