Numerical Analysis and Scientific Computing Seminar | Siddhartha Mishra, Learning PDEs

Tuesday, November 26, 2024 1:00 pm - 2:00 pm EST (GMT -05:00)

Zoom (Please contact ddelreyfernandez@uwaterloo.ca for meeting link) 
 

Speaker

Siddhartha Mishra Professor, Department of Mathematics, ETH Zürich

Title

Learning PDEs

Abstract

Despite their remarkable success over many decades, numerical methods for approximating PDEs can incur a very high computational cost. This limitation has provided impetus to the design of fast and accurate Machine Learning/AI based surrogates which can learn the PDE solution operator from data. In this talk, we review some latest developments in the field of Neural Operators, which are widely used as an ML paradigm for PDEs and discuss state of the art neural operators based on convolutions or attention. The issue of sample complexity is addressed by the design of general purpose Foundation models for PDEs. If time permits, we will also discuss graph based architectures for PDEs on arbitrary domains and conditional Diffusion models for PDEs with multiscale solutions.