09/22/2023
By Joris Roos
Title: Hybrid Iterative Method based on Deep Operator Networks for Solving Differential Equations
Date: Wednesday, Sept. 27
Time: 11 a.m. - Noon
Room: Southwick 313
Abstract: Iterative solver of linear systems is a key component for numerical solutions of differential equations, playing an important role in numerical analysis and scientific computing. While there have been intensive studies on classical methods such as Jacobi, Gauss-Seidel, conjugate gradient, multigrid methods and their more advanced variants, there is still a pressing need to develop faster, more robust, and more reliable solvers. Based on recent advances in scientific deep learning for operator regression, we propose a hybrid numerical solver for solving differential equations. Through a series of numerical experiments, we show that this hybrid solver is capable of providing fast, accurate solutions for a wide class of differential equations, some of which otherwise diverge when using other numerical solvers.