{"ID":2842113,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.10025","arxiv_id":"2511.10025","title":"SVD-NO: Learning PDE Solution Operators with SVD Integral Kernels","abstract":"Neural operators have emerged as a promising paradigm for learning solution operators of partial differential equa- tions (PDEs) directly from data. Existing methods, such as those based on Fourier or graph techniques, make strong as- sumptions about the structure of the kernel integral opera- tor, assumptions which may limit expressivity. We present SVD-NO, a neural operator that explicitly parameterizes the kernel by its singular-value decomposition (SVD) and then carries out the integral directly in the low-rank basis. Two lightweight networks learn the left and right singular func- tions, a diagonal parameter matrix learns the singular values, and a Gram-matrix regularizer enforces orthonormality. As SVD-NO approximates the full kernel, it obtains a high de- gree of expressivity. Furthermore, due to its low-rank struc- ture the computational complexity of applying the operator remains reasonable, leading to a practical system. In exten- sive evaluations on five diverse benchmark equations, SVD- NO achieves a new state of the art. In particular, SVD-NO provides greater performance gains on PDEs whose solutions are highly spatially variable. The code of this work is publicly available at https://github.com/2noamk/SVDNO.git.","short_abstract":"Neural operators have emerged as a promising paradigm for learning solution operators of partial differential equa- tions (PDEs) directly from data. Existing methods, such as those based on Fourier or graph techniques, make strong as- sumptions about the structure of the kernel integral opera- tor, assumptions which ma...","url_abs":"https://arxiv.org/abs/2511.10025","url_pdf":"https://arxiv.org/pdf/2511.10025v1","authors":"[\"Noam Koren\",\"Ralf J. J. Mackenbach\",\"Ruud J. G. van Sloun\",\"Kira Radinsky\",\"Daniel Freedman\"]","published":"2025-11-13T07:02:05Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[]","has_code":false,"code_links":[{"ID":607101,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_id":2842113,"paper_url":"https://arxiv.org/abs/2511.10025","paper_title":"SVD-NO: Learning PDE Solution Operators with SVD Integral Kernels","repo_url":"https://github.com/2noamk/SVDNO.git","is_official":false,"mentioned_in_paper":false,"mentioned_in_github":true,"github_stars":0}]}