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Auto-Adaptive PINNs with Applications to Phase Transitions

arXiv 2510.23999 ↗First posted 28 Oct 2025math.NA cs.LG cs.NAcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 15 of its 33 references that are in the map. First posted on arXiv 28 Oct 2025.

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15 of 33 references.

References · 15

  1. 2019DeepXDE: A deep learning library for solving differential equationscited by 619
  2. 2020B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Datacited by 335
  3. 2020hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decompositioncited by 236
  4. 2022A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networkscited by 236
  5. 2020Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networkscited by 123
  6. 2022Mitigating Propagation Failures in Physics-informed Neural Networks using Retain-Resample-Release (R3) Samplingcited by 73
  7. 2024From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learningcited by 73
  8. 2022Failure-informed adaptive sampling for PINNscited by 64
  9. 2021When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?cited by 58
  10. 2019SoftAdapt: Techniques for Adaptive Loss Weighting of Neural Networks with Multi-Part Loss Functionscited by 40
  11. 2022Adaptive Self-supervision Algorithms for Physics-informed Neural Networkscited by 24
  12. 2022Asymptotic self-similar blow-up profile for three-dimensional axisymmetric Euler equations using neural networkscited by 19
3 more
  1. 2023Failure-informed adaptive sampling for PINNs, Part II: combining with re-sampling and subset simulationcited by 13
  2. 2024Optimal time sampling in physics-informed neural networkscited by 3
  3. 2024Capturing Shock Waves by Relaxation Neural Networkscited by 1

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