Auto-Adaptive PINNs with Applications to Phase Transitions
Numerical Analysis
2026-04-08 v4 Machine Learning
Numerical Analysis
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.
Cite
@article{arxiv.2510.23999,
title = {Auto-Adaptive PINNs with Applications to Phase Transitions},
author = {Kevin Buck and Woojeong Kim},
journal= {arXiv preprint arXiv:2510.23999},
year = {2026}
}
Comments
Accepted for publication in Numerical Mathematics: Theory, Methods and Applications