{"ID":2848864,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.23999","arxiv_id":"2510.23999","title":"Auto-Adaptive PINNs with Applications to Phase Transitions","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.","short_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 reso...","url_abs":"https://arxiv.org/abs/2510.23999","url_pdf":"https://arxiv.org/pdf/2510.23999v4","authors":"[\"Kevin Buck\",\"Woojeong Kim\"]","published":"2025-10-28T02:03:39Z","proceeding":"math.NA","tasks":"[\"math.NA\",\"cs.LG\"]","methods":"[]","has_code":false}