A Curriculum-Training-Based Strategy for Distributing Collocation Points during Physics-Informed Neural Network Training

TL;DR

This paper introduces a curriculum-training-based approach for distributing collocation points in physics-informed neural networks, improving training efficiency and solution quality in multi-dimensional problems.

Contribution

It proposes a novel lightweight collocation point distribution method based on curriculum training, addressing scalability issues in high-dimensional PINN applications.

Findings

Significant reduction in training time.

Enhanced accuracy of the reconstructed MHD solution.

Effective in two-dimensional physics problems.

Abstract

Physics-informed Neural Networks (PINNs) often have, in their loss functions, terms based on physical equations and derivatives. In order to evaluate these terms, the output solution is sampled using a distribution of collocation points. However, density-based strategies, in which the number of collocation points over the domain increases throughout the training period, do not scale well to multiple spatial dimensions. To remedy this issue, we present here a curriculum-training-based method for lightweight collocation point distributions during network training. We apply this method to a PINN which recovers a full two-dimensional magnetohydrodynamic (MHD) solution from a partial sample taken from a baseline MHD simulation. We find that the curriculum collocation point strategy leads to a significant decrease in training time and simultaneously enhances the quality of the reconstructed solution.