Auto-Adaptive PINNs with Applications to Phase Transitions
This work addresses a domain-specific problem in computational physics for researchers using PINNs, presenting an incremental improvement in sampling techniques.
The authors tackled the challenge of accurately resolving interfacial regions in the Allen-Cahn equations using Physics Informed Neural Networks (PINNs) by proposing an adaptive sampling method based on problem-specific heuristics, showing effectiveness over residual-adaptive frameworks in experiments.
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.