Oct 15, 2021

Jianfeng Lu, Duke University

Abstract:

Numerical solution to high dimensional PDEs has been one of the central challenges in scientific computing due to curse of dimension. In recent years, we have seen tremendous progress in applying neural networks to solve high dimensional PDEs, while the analysis for such methods is still lacking. In this talk, we will discuss some of these numerical methods for high dimensional PDEs, challenges and also some initial attempts in numerical analysis for high dimensional elliptic PDEs and eigenvalue problems (based on joint works with Ziang Chen, Yulong Lu, and Min Wang)