# Quasi-Random Physics-informed Neural Networks

arXiv: https://arxiv.org/abs/2507.08121 · HTML: https://mlsanity.com/paper/2507.08121/

## 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.

## Builds on (most cited first, 17 of 17)

- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks](https://mlsanity.com/paper/2207.10289/) (2022)
- [Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics](https://mlsanity.com/paper/1707.09571/) (2017)
- [Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations](https://mlsanity.com/paper/1706.04702/) (2017)
- [Efficient training of physics-informed neural networks via importance sampling](https://mlsanity.com/paper/2104.12325/) (2021)
- [Tackling the Curse of Dimensionality with Physics-Informed Neural Networks](https://mlsanity.com/paper/2307.12306/) (2023)
- [DAS-PINNs: A deep adaptive sampling method for solving high-dimensional partial differential equations](https://mlsanity.com/paper/2112.14038/) (2021)
- [Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations](https://mlsanity.com/paper/1709.05963/) (2017)
- [Failure-informed adaptive sampling for PINNs](https://mlsanity.com/paper/2210.00279/) (2022)
- [PINNACLE: PINN Adaptive ColLocation and Experimental points selection](https://mlsanity.com/paper/2404.07662/) (2024)
- [RoPINN: Region Optimized Physics-Informed Neural Networks](https://mlsanity.com/paper/2405.14369/) (2024)
- [Can Shallow Neural Networks Beat the Curse of Dimensionality? A mean field training perspective](https://mlsanity.com/paper/2005.10815/) (2020)
- [Stochastic Taylor Derivative Estimator: Efficient amortization for arbitrary differential operators](https://mlsanity.com/paper/2412.00088/) (2024)
- [RANG: A Residual-based Adaptive Node Generation Method for Physics-Informed Neural Networks](https://mlsanity.com/paper/2205.01051/) (2022)
- [Heuristic Approaches to Obtain Low-Discrepancy Point Sets via Subset Selection](https://mlsanity.com/paper/2306.15276/) (2023)
- [Constructing Low Star Discrepancy Point Sets with Genetic Algorithms](https://mlsanity.com/paper/1304.1978/) (2013)
- [A Nonlocal Functional Promoting Low-Discrepancy Point Sets](https://mlsanity.com/paper/1902.00441/) (2019)

## 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.