GAS: A Gaussian Mixture Distribution-Based Adaptive Sampling Method for PINNs
This addresses accuracy issues in PINNs for scientific computation, offering an incremental improvement for researchers in computational physics and machine learning.
The paper tackles the low accuracy of Physics-Informed Neural Networks (PINNs) for solving partial differential equations, especially in irregular problems, by proposing GAS, an adaptive sampling method that uses residual information to improve training; numerical simulations on 2D and 10D problems show it achieves state-of-the-art accuracy among deep solvers and is comparable to traditional methods.
With the recent study of deep learning in scientific computation, the Physics-Informed Neural Networks (PINNs) method has drawn widespread attention for solving Partial Differential Equations (PDEs). Compared to traditional methods, PINNs can efficiently handle high-dimensional problems, but the accuracy is relatively low, especially for highly irregular problems. Inspired by the idea of adaptive finite element methods and incremental learning, we propose GAS, a Gaussian mixture distribution-based adaptive sampling method for PINNs. During the training procedure, GAS uses the current residual information to generate a Gaussian mixture distribution for the sampling of additional points, which are then trained together with historical data to speed up the convergence of the loss and achieve higher accuracy. Several numerical simulations on 2D and 10D problems show that GAS is a promising method that achieves state-of-the-art accuracy among deep solvers, while being comparable with traditional numerical solvers.