GAS: A Gaussian Mixture Distribution-Based Adaptive Sampling Method for PINNs
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With recent study of the deep learning in scientific computation, the PINNs method has drawn widespread attention for solving PDEs. Compared with traditional methods, PINNs can efficiently handle high-dimensional problems, while 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 history data to speed up the convergence of loss and achieve a higher accuracy. Several numerical simulations on 2d to 10d problems show that GAS is a promising method which achieves the state-of-the-art accuracy among deep solvers, while being comparable with traditional numerical solvers.
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