Learning dissipation and instability fields from chaotic dynamics
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866916598700310528 |
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| author | Giorgini, Ludovico T Souza, Andre N Lippolis, Domenico Cvitanović, Predrag Schmid, Peter |
| author_facet | Giorgini, Ludovico T Souza, Andre N Lippolis, Domenico Cvitanović, Predrag Schmid, Peter |
| contents | To make predictions or design control, information on local sensitivity of initial conditions and state-space contraction is both central, and often instrumental. However, it is not always simple to reliably determine instability fields or local dissipation rates, due to computational challenges or ignorance of the governing equations. Here, we construct an alternative route towards that goal, by estimating the Jacobian of a discrete-time dynamical system locally from the entries of the transition matrix that approximates the Perron-Frobenius operator for a given state-space partition. Numerical tests on one- and two-dimensional chaotic maps show promising results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03456 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Learning dissipation and instability fields from chaotic dynamics Giorgini, Ludovico T Souza, Andre N Lippolis, Domenico Cvitanović, Predrag Schmid, Peter Chaotic Dynamics To make predictions or design control, information on local sensitivity of initial conditions and state-space contraction is both central, and often instrumental. However, it is not always simple to reliably determine instability fields or local dissipation rates, due to computational challenges or ignorance of the governing equations. Here, we construct an alternative route towards that goal, by estimating the Jacobian of a discrete-time dynamical system locally from the entries of the transition matrix that approximates the Perron-Frobenius operator for a given state-space partition. Numerical tests on one- and two-dimensional chaotic maps show promising results. |
| title | Learning dissipation and instability fields from chaotic dynamics |
| topic | Chaotic Dynamics |
| url | https://arxiv.org/abs/2502.03456 |