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

2021/03/19 by Z. Fang, Fang, Zhiwei, Justin Zhan +3
Engineering · Physics and Astronomy · #Electromagnetic Simulation and Numerical Methods #FOS: Computer and information sciences #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2103.13878

openalex publication_date 2021/03/19 · openalex created_date 2021/03/29 · openalex updated_date 2026/07/28

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.

Citations

• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• hp-VPINNs: Variational physics-informed neural networks with domain decomposition

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