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

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.

References in corpus (6)

• hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition
• Adversarial Uncertainty Quantification in Physics-Informed Neural Networks
• Variational Physics-Informed Neural Networks For Solving Partial Differential Equations
• An RBF-FD closest point method for solving PDEs on surfaces
• A least-squares implicit RBF-FD closest point method and applications to PDEs on moving surfaces
• PDEs on moving surfaces via the closest point method and a modified grid based particle method

Cited by in corpus (2)

• $\Delta$-PINNs: physics-informed neural networks on complex geometries
• A shallow physics-informed neural network for solving partial differential equations on surfaces