A Physics-Informed Neural Network Framework For Partial Differential Equations on 3D Surfaces: Time-Dependent Problems

Zhiwei Fang, Justin Z. Zhan, Xiu Yang

Abstract: In this paper, we show a physics-informed neural network solver for the time-dependent surface PDEs. Unlike the traditional numerical solver, no extension of PDE and mesh on the surface is needed. We show a simplified prior estimate of the surface differential operators so that PINN's loss value will be an indicator of the residue of the surface PDEs. Numerical experiments verify efficacy of our algorithm.