Quasi-Random Physics-informed Neural Networks

• URL: http://arxiv.org/abs/2507.08121v1
• Date: Thu, 10 Jul 2025 19:15:43 GMT
• Title: Quasi-Random Physics-informed Neural Networks
• Authors: Tianchi Yu, Ivan Oseledets,
• Abstract summary: This paper proposes Quasi-Random Physics-Informed Neural Networks (QRPINNs), which use low-discrepancy sequences for sampling instead of random points directly from the domain.<n>Experiments demonstrate that QRPINNs significantly outperform PINNs and some representative adaptive sampling methods, especially in high-dimensional PDEs.
• Score: 4.347494885647007
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Physics-informed neural networks have shown promise in solving partial differential equations (PDEs) by integrating physical constraints into neural network training, but their performance is sensitive to the sampling of points. Based on the impressive performance of quasi Monte-Carlo methods in high dimensional problems, this paper proposes Quasi-Random Physics-Informed Neural Networks (QRPINNs), which use low-discrepancy sequences for sampling instead of random points directly from the domain. Theoretically, QRPINNs have been proven to have a better convergence rate than PINNs. Empirically, experiments demonstrate that QRPINNs significantly outperform PINNs and some representative adaptive sampling methods, especially in high-dimensional PDEs. Furthermore, combining QRPINNs with adaptive sampling can further improve the performance.

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