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Quasi-Random Physics-informed Neural Networks

arXiv 2507.08121 ↗First posted 10 Jul 2025cs.LG cs.AI cs.NAcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 17 of its 61 references that are in the map. First posted on arXiv 10 Jul 2025.

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References · 17

  1. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 634
  2. 2022A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networkscited by 236
  3. 2017Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanicscited by 214
  4. 2017Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equationscited by 191
  5. 2021Efficient training of physics-informed neural networks via importance samplingcited by 110
  6. 2023Tackling the Curse of Dimensionality with Physics-Informed Neural Networkscited by 79
  7. 2021DAS-PINNs: A deep adaptive sampling method for solving high-dimensional partial differential equationscited by 66
  8. 2017Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equationscited by 65
  9. 2022Failure-informed adaptive sampling for PINNscited by 64
  10. 2024PINNACLE: PINN Adaptive ColLocation and Experimental points selectioncited by 32
  11. 2024RoPINN: Region Optimized Physics-Informed Neural Networkscited by 26
  12. 2020Can Shallow Neural Networks Beat the Curse of Dimensionality? A mean field training perspectivecited by 22
5 more
  1. 2024Stochastic Taylor Derivative Estimator: Efficient amortization for arbitrary differential operatorscited by 20
  2. 2022RANG: A Residual-based Adaptive Node Generation Method for Physics-Informed Neural Networkscited by 14
  3. 2023Heuristic Approaches to Obtain Low-Discrepancy Point Sets via Subset Selectioncited by 5
  4. 2013Constructing Low Star Discrepancy Point Sets with Genetic Algorithmscited by 2
  5. 2019A Nonlocal Functional Promoting Low-Discrepancy Point Setscited by 1

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