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Auto-Adaptive PINNs with Applications to Phase Transitions

Published: October 28, 2025 | arXiv ID: 2510.23999v2

By: Kevin Buck, Woojeong Kim

Potential Business Impact:

Teaches computers to solve hard math problems better.

Business Areas:
Predictive Analytics Artificial Intelligence, Data and Analytics, Software

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.

Country of Origin
🇺🇸 United States

Page Count
15 pages

Category
Mathematics:
Numerical Analysis (Math)