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Number Theoretic Accelerated Learning of Physics-Informed Neural Networks

arXiv 2307.13869 ↗First posted 26 Jul 2023cs.LG cs.NA math.NAcited by 0

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Abstract (arXiv)

Physics-informed neural networks solve partial differential equations by training neural networks. Since this method approximates infinite-dimensional PDE solutions with finite collocation points, minimizing discretization errors by selecting suitable points is essential for accelerating the learning process. Inspired by number theoretic methods for numerical analysis, we introduce good lattice training and periodization tricks, which ensure the conditions required by the theory. Our experiments demonstrate that GLT requires 2-7 times fewer collocation points, resulting in lower computational cost, while achieving competitive performance compared to typical sampling methods.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 19 of its 45 references that are in the map. First posted on arXiv 26 Jul 2023.

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References · 19

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7 more
  1. 2022Applications of physics informed neural operatorscited by 33
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