Auto-Adaptive PINNs with Applications to Phase Transitions

TL;DR

This paper introduces an adaptive sampling technique for Physics Informed Neural Networks (PINNs) that improves resolution of phase transition regions, demonstrated on Allen-Cahn equations.

Contribution

It presents a novel adaptive sampling method based on problem-specific heuristics, enhancing PINN training without post-hoc resampling.

Findings

The method effectively resolves interfacial regions in Allen-Cahn equations.

It outperforms residual-adaptive frameworks in experiments.

Abstract

We propose an adaptive sampling method for the training of Physics Informed Neural Networks (PINNs) which allows for sampling based on an arbitrary problem-specific heuristic which may depend on the network and its gradients. In particular we focus our analysis on the Allen-Cahn equations, attempting to accurately resolve the characteristic interfacial regions using a PINN without any post-hoc resampling. In experiments, we show the effectiveness of these methods over residual-adaptive frameworks.