Date/Time
Date(s) - 07/11/2022
11:30 am - 12:30 pm

Speaker: Saad Qadeer (Pacific Northwest National Lab)

Title: A spectral approach for time-dependent PDEs using machine-learned basis functions

Abstract: A major obstacle in the deployment of spectral methods is the choice of appropriate bases for trial and test spaces. If chosen suitably, these basis functions lead invariably to well-posed discretized problems and well-conditioned linear systems, while the resulting approximate solutions are provably high-order accurate. However, barring domain decomposition approaches, devising such functions for arbitrary geometries from scratch is a hugely challenging task. Fortunately, the recently developed DeepONet approach for approximating solution operators suggests a highly promising device for generating machine-learned basis functions. In this talk, we propose a Galerkin approach for time-dependent PDEs that is powered by basis functions gleaned from the DeepONet architecture. We shall outline our procedure for obtaining these basis functions and detail their many favourable properties. Next, we shall present the results of numerical tests for various problems, including advection, advection-diffusion, viscous Burgers’, Korteweg-De Vries, and Kuramoto-Sivashinsky equations. Finally, we will identify potential obstacles in the course of generalization to higher dimensions and suggest possible remedies.

Location: Virtual 

Zoom Link: https://mcmaster.zoom.us/j/94822925263?pwd=SitnUVpvQldERlpsMWdHZzZRTjlyZz09