Physics-Informed Neural Networks for Irregular Domain Mapping and Partial Differential Equations solving

TL;DR

This paper introduces a physics-informed neural network approach that maps irregular domains to regular grids, enabling efficient PDE solving with finite difference methods on structured grids.

Contribution

It presents a novel method for domain mapping using PINNs, allowing PDEs on irregular domains to be solved on regular grids, improving flexibility and computational efficiency.

Findings

PINNs can effectively map irregular to regular domains.

Structured grids facilitate PDE solving on irregular boundaries.

The approach enhances computational versatility for PDEs.

Abstract

The solution of partial differential equations (PDES) on irregular domains has long been a subject of significant research interest. In this work, we present an approach utilizing physics-informed neural networks (PINNs) to achieve irregular-to-regular domain mapping. Thus we can use finite difference method and physics-informed convolutional neural networks to solve PDEs on rectangular grids instead of the original irregular boundary. Structured grids on irregular domains are obtained by inverse mapping. We demonstrate PINN's versatile capability to produce customized structured grids tailored to diverse computational requirements, thereby significantly facilitating PDEs solving.