Physics Informed Neural Networks for heat conduction with phase change

TL;DR

This paper explores the application of Physics Informed Neural Networks (PINNs) to solve the Stefan problem, a PDE modeling heat transfer with phase change, addressing challenges near phase interfaces and comparing with classical methods.

Contribution

The paper introduces strategies to improve PINNs for phase change problems and compares their performance with traditional PDE solvers.

Findings

PINNs can effectively model heat conduction with phase change.

Different strategies improve PINN learning near phase interfaces.

PINNs show competitive accuracy compared to finite difference methods.

Abstract

We study numerical algorithms to solve a specific Partial Differential Equation (PDE), namely the Stefan problem, using Physics Informed Neural Networks (PINNs). This problem describes the heat propagation in a liquid-solid phase change system. It implies a heat equation and a discontinuity at the interface where the phase change occurs. In the context of PINNs, this model leads to difficulties in the learning process, especially near the interface of phase change. We present different strategies that can be used in this context. We illustrate our results and compare with classical solvers for PDEs (finite differences).