الملخص
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.
الكلمات المفتاحية
الموضوع
بيانات النشر
- المجلة
- غير متاح
- وصول مفتوح
- وصول مفتوح أخضر
اقتبس هذه المقالة
APA 7
Molina, J., Perdikaris, P., Petrache, M., Courdurier, M., & Costabal, F. S. (2026). Operator-informed initialization for Fourier features physics-informed neural networks. https://omanscience.com/ar/articles/operator-informed-initialization-for-fourier-features-physics-informed-neural-networks
MLA 9
Molina, Juan, et al. "Operator-informed initialization for Fourier features physics-informed neural networks." https://omanscience.com/ar/articles/operator-informed-initialization-for-fourier-features-physics-informed-neural-networks.
شيكاغو (المؤلف–التاريخ)
Molina, Juan, Paris Perdikaris, Mircea Petrache, Matías Courdurier, and Francisco Sahli Costabal. 2026. "Operator-informed initialization for Fourier features physics-informed neural networks." https://omanscience.com/ar/articles/operator-informed-initialization-for-fourier-features-physics-informed-neural-networks.
هارفارد
Molina, J., Perdikaris, P., Petrache, M., Courdurier, M. and Costabal, F. S. (2026) 'Operator-informed initialization for Fourier features physics-informed neural networks', Available at: https://omanscience.com/ar/articles/operator-informed-initialization-for-fourier-features-physics-informed-neural-networks.
فانكوفر
Molina J, Perdikaris P, Petrache M, Courdurier M, Costabal FS. Operator-informed initialization for Fourier features physics-informed neural networks. https://omanscience.com/ar/articles/operator-informed-initialization-for-fourier-features-physics-informed-neural-networks
IEEE
J. Molina, P. Perdikaris, M. Petrache, M. Courdurier, and F. S. Costabal, "Operator-informed initialization for Fourier features physics-informed neural networks," https://omanscience.com/ar/articles/operator-informed-initialization-for-fourier-features-physics-informed-neural-networks.