Grad-RAR: An Adaptive Sampling Method Based on Residual Gradient for Physical-Informed Neural Networks

Abstract

PINNs, as a new method for solving PDEs, can embed PDEs as a prior into neural networks for training. The distribution of sample residual points has a strong influence on the solution accuracy of PINNs. In this paper, we propose an adaptive sampling algorithm based on the residuals and its gradient characters (Grad-RAR), which utilizes the residuals of sample points to obtain their gradient information and retain sample residual points with special gradients, and combines it with a probabilistic sampling model (RAR-D) to achieve effective sampling in the computational domain. We test the performance of multiple sampling methods for two forward problems and one inverse problem, and the study shows that our proposed adaptive sampling method performs better compared to existing sampling methods.