Efficient Training of Physics-Informed Neural Networks with Direct Grid Refinement Algorithm

TL;DR

This paper introduces a novel direct mesh refinement algorithm for adaptive sampling in Physics-Informed Neural Networks, significantly improving computational efficiency and simulation accuracy over existing methods.

Contribution

The paper proposes an innovative direct mesh refinement algorithm for adaptive sampling in PINNs, addressing limitations of previous techniques and enhancing performance.

Findings

Better agreement with benchmark models

Superior performance with higher refinement factors

Enhanced simulation accuracy

Abstract

This research presents the development of an innovative algorithm tailored for the adaptive sampling of residual points within the framework of Physics-Informed Neural Networks (PINNs). By addressing the limitations inherent in existing adaptive sampling techniques, our proposed methodology introduces a direct mesh refinement approach that effectively ensures both computational efficiency and adaptive point placement. Verification studies were conducted to evaluate the performance of our algorithm, showcasing reasonable agreement between the model based on our novel approach and benchmark model results. Comparative analyses with established adaptive resampling techniques demonstrated the superior performance of our approach, particularly when implemented with higher refinement factor. Overall, our findings highlight the enhancement of simulation accuracy achievable through the application of our adaptive sampling algorithm for Physics-Informed Neural Networks.