Physics Informed Random Feature Neural Networks for Solving PDEs
Abstract
Machine learning-based partial differential equations (PDEs) solvers have attracted significant attention in recent years. Most progress in this area has been driven by deep neural networks such as physics-informed neural networks (PINNs) and kernel method (such as physics-informed Gaussian Processes). We introduce a physics-informed random feature method for countering part of the spectral bias which PINN-based solvers are facing for a certain class of PDEs. Random feature method was originally proposed to approximate large-scale kernel machines and can be viewed as a specialized randomized neural network. Compared to other state-of-the-art PINN-based solvers which require a large number of collocation points, our proposed method reduces the computational complexity. In this paper, we develop a rigorous approximation error analysis and derive high-probability error bounds on the H1 norm. We provide extensive numerical tests for verifying our theoretical guarantees on error decay rates, as well as several comparison tests to showcase our claimed capability for combating spectral bias in these deep learning based methods.
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BibTeX
@misc{chen2026physics,
title = {{Physics Informed Random Feature Neural Networks for Solving PDEs}},
author = {Chi-An Chen and Chunyang Liao and Ming Zhong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16406},
eprint = {2609.16406},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16406},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Physics Informed Random Feature Neural Networks for Solving PDEs
AU - Chi-An Chen
AU - Chunyang Liao
AU - Ming Zhong
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.16406
UR - https://arxiv.org/abs/2609.16406
AB - Machine learning-based partial differential equations (PDEs) solvers have attracted significant attention in recent years. Most progress in this area has been driven by deep neural networks such as physics-informed neural networks (PINNs) and kernel method (such as physics-informed Gaussian Processes). We introduce a physics-informed random feature method for countering part of the spectral bias which PINN-based solvers are facing for a certain class of PDEs. Random feature method was originally proposed to approximate large-scale kernel machines and can be viewed as a specialized randomized neural network. Compared to other state-of-the-art PINN-based solvers which require a large number of collocation points, our proposed method reduces the computational complexity. In this paper, we develop a rigorous approximation error analysis and derive high-probability error bounds on the H^1 norm. We provide extensive numerical tests for verifying our theoretical guarantees on error decay rates, as well as several comparison tests to showcase our claimed capability for combating spectral bias in these deep learning based methods.
ER -