KANO: Kolmogorov-Arnold Neural Operator
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910032270983168 |
|---|---|
| author | Lee, Jin Liu, Ziming Yu, Xinling Wang, Yixuan Jeong, Haewon Niu, Murphy Yuezhen Zhang, Zheng |
| author_facet | Lee, Jin Liu, Ziming Yu, Xinling Wang, Yixuan Jeong, Haewon Niu, Murphy Yuezhen Zhang, Zheng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16825 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | KANO: Kolmogorov-Arnold Neural Operator Lee, Jin Liu, Ziming Yu, Xinling Wang, Yixuan Jeong, Haewon Niu, Murphy Yuezhen Zhang, Zheng Machine Learning Artificial Intelligence Computational Engineering, Finance, and Science 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. |
| title | KANO: Kolmogorov-Arnold Neural Operator |
| topic | Machine Learning Artificial Intelligence Computational Engineering, Finance, and Science |
| url | https://arxiv.org/abs/2509.16825 |