Maximum-likelihood reprojections for reliable Koopman-based predictions and bifurcation analysis of parametric dynamical systems
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909656167743488 |
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| author | van Goor, Pieter Mahony, Robert Schaller, Manuel Worthmann, Karl |
| author_facet | van Goor, Pieter Mahony, Robert Schaller, Manuel Worthmann, Karl |
| contents | Koopman-based methods leverage a nonlinear lifting to enable linear regression techniques. Consequently, data generation, learning and prediction is performed through the lens of this lifting, giving rise to a nonlinear manifold that is invariant under the Koopman operator. In data-driven approximation such as Extended Dynamic Mode Decomposition, this invariance is typically lost due to the presence of (finite-data) approximation errors. In this work, we show that reprojections are crucial for reliable predictions. We provide an approach via closest-point projections that ensure consistency with this nonlinear manifold, which is strongly related to a Riemannian metric and maximum likelihood estimates. While these results are already novel for autonomous systems, we present our approach for parametric systems, providing the basis for data-driven bifurcation analysis and control applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_17817 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximum-likelihood reprojections for reliable Koopman-based predictions and bifurcation analysis of parametric dynamical systems van Goor, Pieter Mahony, Robert Schaller, Manuel Worthmann, Karl Dynamical Systems Systems and Control Koopman-based methods leverage a nonlinear lifting to enable linear regression techniques. Consequently, data generation, learning and prediction is performed through the lens of this lifting, giving rise to a nonlinear manifold that is invariant under the Koopman operator. In data-driven approximation such as Extended Dynamic Mode Decomposition, this invariance is typically lost due to the presence of (finite-data) approximation errors. In this work, we show that reprojections are crucial for reliable predictions. We provide an approach via closest-point projections that ensure consistency with this nonlinear manifold, which is strongly related to a Riemannian metric and maximum likelihood estimates. While these results are already novel for autonomous systems, we present our approach for parametric systems, providing the basis for data-driven bifurcation analysis and control applications. |
| title | Maximum-likelihood reprojections for reliable Koopman-based predictions and bifurcation analysis of parametric dynamical systems |
| topic | Dynamical Systems Systems and Control |
| url | https://arxiv.org/abs/2506.17817 |