{"ID":2887978,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.00628","arxiv_id":"2508.00628","title":"Separated-Variable Spectral Neural Networks: A Physics-Informed Learning Approach for High-Frequency PDEs","abstract":"Solving high-frequency oscillatory partial differential equations (PDEs) is a critical challenge in scientific computing, with applications in fluid mechanics, quantum mechanics, and electromagnetic wave propagation. Traditional physics-informed neural networks (PINNs) suffer from spectral bias, limiting their ability to capture high-frequency solution components. We introduce Separated-Variable Spectral Neural Networks (SV-SNN), a novel framework that addresses these limitations by integrating separation of variables with adaptive spectral methods. Our approach features three key innovations: (1) decomposition of multivariate functions into univariate function products, enabling independent spatial and temporal networks; (2) adaptive Fourier spectral features with learnable frequency parameters for high-frequency capture; and (3) theoretical framework based on singular value decomposition to quantify spectral bias. Comprehensive evaluation on benchmark problems including Heat equation, Helmholtz equation, Poisson equations and Navier-Stokes equations demonstrates that SV-SNN achieves 1-3 orders of magnitude improvement in accuracy while reducing parameter count by over 90\\% and training time by 60\\%. These results establish SV-SNN as an effective solution to the spectral bias problem in neural PDE solving. The implementation will be made publicly available upon acceptance at https://github.com/xgxgnpu/SV-SNN.","short_abstract":"Solving high-frequency oscillatory partial differential equations (PDEs) is a critical challenge in scientific computing, with applications in fluid mechanics, quantum mechanics, and electromagnetic wave propagation. Traditional physics-informed neural networks (PINNs) suffer from spectral bias, limiting their ability...","url_abs":"https://arxiv.org/abs/2508.00628","url_pdf":"https://arxiv.org/pdf/2508.00628v1","authors":"[\"Xiong Xiong\",\"Zhuo Zhang\",\"Rongchun Hu\",\"Chen Gao\",\"Zichen Deng\"]","published":"2025-08-01T13:40:10Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[]","has_code":false,"code_links":[{"ID":611494,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_id":2887978,"paper_url":"https://arxiv.org/abs/2508.00628","paper_title":"Separated-Variable Spectral Neural Networks: A Physics-Informed Learning Approach for High-Frequency PDEs","repo_url":"https://github.com/xgxgnpu/SV-SNN","is_official":false,"mentioned_in_paper":false,"mentioned_in_github":true,"github_stars":0}]}