Neural Operator

Neural Operators: Theory, Architecture, and Applications for PDEs

Xinliang Liu, Postdoctoral Research Fellow, Applied Mathematics and Computational Sciences

Apr 16, 16:00 - 17:00

B1 L3 R3119

Neural Operator Multigrid

Abstract Neural operator methods provide a novel approach for solving or learning the complex mappings from parameters to solutions arising from intricate physical systems. In this talk, I will cover the foundational aspects of neural operators, encompassing both theoretical frameworks and algorithmic developments, including some well-known neural operator architectures. Additionally, I will share our recent work on applying the neural operator method to multiscale partial differential equations (PDEs). To tackle the challenges of multiscale PDEs, we have developed a neural operator with a