Using good lattice points as training points for physics-informed neural networks gives lower errors on low-regularity and high-dimensional PDEs, with a quadrature error of O((log N)^d/N) versus O(N^{-1/2}) for random sampling.
Agent-physics-informed neural network solving frequency-domain helmholtz equation related forward and inverse problems
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A novel number-theoretic sampling method for neural network solutions of partial differential equations
Using good lattice points as training points for physics-informed neural networks gives lower errors on low-regularity and high-dimensional PDEs, with a quadrature error of O((log N)^d/N) versus O(N^{-1/2}) for random sampling.