Koopman Regularization
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917289362718720 |
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| author | Cohen, Ido |
| author_facet | Cohen, Ido |
| contents | \emph{Koopman Regularization} is a constrained optimization-based method to learn the governing equations from sparse and corrupted samples of the vector field. \emph{Koopman Regularization} extracts a functionally independent set of Koopman Eigenfunctions from the samples. This set implements the principle of parsimony, since, even though its cardinality is finite, it restores the dynamics precisely.
\emph{Koopman Regularization} formulates the Koopman Partial Differential Equation as the objective function and the condition of functional independence as the feasible region. Then, this work suggests a barrier method-based algorithm to solve this constrained optimization problem that yields promising results in denoising, generalization, and dimensionality reduction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11302 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Koopman Regularization Cohen, Ido Dynamical Systems Differential Geometry \emph{Koopman Regularization} is a constrained optimization-based method to learn the governing equations from sparse and corrupted samples of the vector field. \emph{Koopman Regularization} extracts a functionally independent set of Koopman Eigenfunctions from the samples. This set implements the principle of parsimony, since, even though its cardinality is finite, it restores the dynamics precisely. \emph{Koopman Regularization} formulates the Koopman Partial Differential Equation as the objective function and the condition of functional independence as the feasible region. Then, this work suggests a barrier method-based algorithm to solve this constrained optimization problem that yields promising results in denoising, generalization, and dimensionality reduction. |
| title | Koopman Regularization |
| topic | Dynamical Systems Differential Geometry |
| url | https://arxiv.org/abs/2403.11302 |