{"ID":2868513,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.16825","arxiv_id":"2509.16825","title":"KANO: Kolmogorov-Arnold Neural Operator","abstract":"We introduce Kolmogorov--Arnold Neural Operator (KANO), a dual-domain neural operator jointly parameterized by both spectral and spatial bases with intrinsic symbolic interpretability. We theoretically demonstrate that KANO overcomes the pure-spectral bottleneck of Fourier Neural Operator (FNO): KANO remains expressive over generic position-dependent dynamics (variable coefficient PDEs) for any physical input, whereas FNO stays practical only for spectrally sparse operators and strictly imposes a fast-decaying input Fourier tail. We verify our claims empirically on position-dependent differential operators, for which KANO robustly generalizes but FNO fails to. In the quantum Hamiltonian learning benchmark, KANO reconstructs ground-truth Hamiltonians in closed-form symbolic representations accurate to the fourth decimal place in coefficients and attains $\\approx 6\\times10^{-6}$ state infidelity from projective measurement data, substantially outperforming that of the FNO trained with ideal full wave function data, $\\approx 1.5\\times10^{-2}$, by orders of magnitude.","short_abstract":"We introduce Kolmogorov--Arnold Neural Operator (KANO), a dual-domain neural operator jointly parameterized by both spectral and spatial bases with intrinsic symbolic interpretability. We theoretically demonstrate that KANO overcomes the pure-spectral bottleneck of Fourier Neural Operator (FNO): KANO remains expressive...","url_abs":"https://arxiv.org/abs/2509.16825","url_pdf":"https://arxiv.org/pdf/2509.16825v6","authors":"[\"Jin Lee\",\"Ziming Liu\",\"Xinling Yu\",\"Yixuan Wang\",\"Haewon Jeong\",\"Murphy Yuezhen Niu\",\"Zheng Zhang\"]","published":"2025-09-20T22:32:58Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\",\"cs.CE\"]","methods":"[]","has_code":false}