Solving PDEs on Manifold With Machine Learning

By Senwei Liang, Shixiao Jiang, John Harlim, Haizhao Yang

Introduction

The repository is the implementation of the paper "Solving PDEs on Unknown Manifolds With Machine Learning" [paper]. The basic idea is to approximate the differential operator by diffusion maps, and then we apply a deep neural network to solve the discretized system.

Requirement

• Matlab
• Python 3.6 and Pytorch