arXiv：cs.LG· Juan Molina, Paris Perdikaris, Mircea Petrache, Mat\'ias Courdurier, Francisco Sahli Costabal·· 3 小时前AI 评分32
面向傅里叶特征 PINN 的算子感知初始化方法
Operator-informed initialization for Fourier features physics-informed neural networks
AI 导读
研究者针对傅里叶特征物理信息神经网络（PINN）的谱偏置问题，在神经正切核（NTK）框架下推导出频域残差演化方程，发现特定频率的收敛速度主要由微分算子符号与初始化权重谱密度的乘积决定。据此提出一种算子感知初始化策略，按所求解 PDE 定制初始权重分布，在不增加训练成本的前提下平衡各频率收敛速度并提升预测精度，在线性与非线性 PDE 数值实验中均优于标准初始化。
正文
Abstract:Physics-Informed Neural Networks (PINNs) typically exhibit spectral bias, where some frequencies of the target function converge more slowly than others. In this work, we analyze the training dynamics of Fourier Feature PINNs in the Neural Tangent Kernel regime to address this limitation. We derive an explicit evolution equation to estimate the residual error in the frequency domain, demonstrating that the convergence rate of specific frequencies is primarily governed by the product of the differential operator's symbol and the spectral density of the initialization weights. Leveraging this theoretical insight, we propose an informative initialization strategy that tailors the initial weight distribution to the specific PDE being solved. With this method, we can diminish the operator-induced spectral bias, balancing the convergence rates across the frequency spectrum and achieving better prediction accuracy. Numerical experiments on linear and nonlinear partial differential equations confirm that this initialization strategy improves learning dynamics and approximation accuracy across frequencies compared to standard initialization methods, with no additional training cost.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.03378 [cs.LG] |
| (or arXiv:2610.03378v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.03378 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Francisco Sahli Costabal [view email]
[v1]
Fri, 2 Oct 2026 14:32:40 UTC (6,768 KB)
来源：arXiv：cs.LG · arxiv.org