Spatio-Temporal Prediction via Operator-Valued RKHS and Koopman Approximation
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915999432835072 |
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| author | Withanachchi, Mahishanka |
| author_facet | Withanachchi, Mahishanka |
| contents | We develop a comprehensive framework for spatio-temporal prediction of time-varying vector fields using operator-valued reproducing kernel Hilbert spaces (OV RKHS). By integrating Sobolev regularity with Koopman operator theory, we establish representer theorems, approximation rates, and spectral convergence results for kernel-based learning of dynamical systems. Our theoretical contributions include new representer theorems for time-aligned OV RKHS interpolation, Sobolev approximation bounds for smooth vector fields, kernel Koopman operator approximations, and spectral convergence guarantees. These results underpin data-driven reduced-order modeling and forecasting for complex nonlinear dynamical systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12474 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spatio-Temporal Prediction via Operator-Valued RKHS and Koopman Approximation Withanachchi, Mahishanka General Mathematics We develop a comprehensive framework for spatio-temporal prediction of time-varying vector fields using operator-valued reproducing kernel Hilbert spaces (OV RKHS). By integrating Sobolev regularity with Koopman operator theory, we establish representer theorems, approximation rates, and spectral convergence results for kernel-based learning of dynamical systems. Our theoretical contributions include new representer theorems for time-aligned OV RKHS interpolation, Sobolev approximation bounds for smooth vector fields, kernel Koopman operator approximations, and spectral convergence guarantees. These results underpin data-driven reduced-order modeling and forecasting for complex nonlinear dynamical systems. |
| title | Spatio-Temporal Prediction via Operator-Valued RKHS and Koopman Approximation |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2507.12474 |