Toeplitz Based Spectral Methods for Data-driven Dynamical Systems
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| author | Kostic, Vladimir R. Lounici, Karim Pontil, Massimiliano |
| author_facet | Kostic, Vladimir R. Lounici, Karim Pontil, Massimiliano |
| contents | We introduce a Toeplitz-based framework for data-driven spectral estimation of linear evolution operators in dynamical systems. Focusing on transfer and Koopman operators from equilibrium trajectories without access to the underlying equations of motion, our method applies Toeplitz filters to the infinitesimal generator to extract eigenvalues, eigenfunctions, and spectral measures. Structural prior knowledge, such as self-adjointness or skew-symmetry, can be incorporated by design. The approach is statistically consistent and computationally efficient, leveraging both primal and dual algorithms commonly used in statistical learning. Numerical experiments on deterministic and chaotic systems demonstrate that the framework can recover spectral properties beyond the reach of standard data-driven methods. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_09791 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Toeplitz Based Spectral Methods for Data-driven Dynamical Systems Kostic, Vladimir R. Lounici, Karim Pontil, Massimiliano Dynamical Systems Machine Learning Numerical Analysis 65F15 (Primary) 65F30 68T09 (Secondary) We introduce a Toeplitz-based framework for data-driven spectral estimation of linear evolution operators in dynamical systems. Focusing on transfer and Koopman operators from equilibrium trajectories without access to the underlying equations of motion, our method applies Toeplitz filters to the infinitesimal generator to extract eigenvalues, eigenfunctions, and spectral measures. Structural prior knowledge, such as self-adjointness or skew-symmetry, can be incorporated by design. The approach is statistically consistent and computationally efficient, leveraging both primal and dual algorithms commonly used in statistical learning. Numerical experiments on deterministic and chaotic systems demonstrate that the framework can recover spectral properties beyond the reach of standard data-driven methods. |
| title | Toeplitz Based Spectral Methods for Data-driven Dynamical Systems |
| topic | Dynamical Systems Machine Learning Numerical Analysis 65F15 (Primary) 65F30 68T09 (Secondary) |
| url | https://arxiv.org/abs/2602.09791 |