Auto-Adaptive PINNs with Applications to Phase Transitions

• URL: http://arxiv.org/abs/2510.23999v2
• Date: Wed, 29 Oct 2025 14:38:26 GMT
• Title: Auto-Adaptive PINNs with Applications to Phase Transitions
• Abstract summary: We propose an adaptive sampling method for the training of Physics Informed Neural Networks (PINNs)<n>In particular we focus on the Allen-Cahn equations, attempting to accurately resolve the characteristic interfacial regions using a PINN without any post-hoc resampling.<n>In experiments, we show the effectiveness of these methods over residual-adaptive frameworks.
• Score: 2.0973794455886545
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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