Reduced Markovian Models of Dynamical Systems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866929339894857728 |
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| author | Giorgini, Ludovico Theo Souza, Andre N. Schmid, Peter J. |
| author_facet | Giorgini, Ludovico Theo Souza, Andre N. Schmid, Peter J. |
| contents | Leveraging recent work on data-driven methods for constructing a finite state space Markov process from dynamical systems, we address two problems for obtaining further reduced statistical representations. The first problem is to extract the most salient reduced-order dynamics for a given timescale by using a modified clustering algorithm from network theory. The second problem is to provide an alternative construction for the infinitesimal generator of a Markov process that respects statistical features over a large range of timescales. We demonstrate the methodology on three low-dimensional dynamical systems with stochastic and chaotic dynamics. We then apply the method to two high-dimensional dynamical systems, the Kuramoto-Sivashinky equations and data sampled from fluid-flow experiments via Particle-Image Velocimetry. We show that the methodology presented herein provides a robust reduced-order statistical representation of the underlying system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_10864 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Reduced Markovian Models of Dynamical Systems Giorgini, Ludovico Theo Souza, Andre N. Schmid, Peter J. Chaotic Dynamics Leveraging recent work on data-driven methods for constructing a finite state space Markov process from dynamical systems, we address two problems for obtaining further reduced statistical representations. The first problem is to extract the most salient reduced-order dynamics for a given timescale by using a modified clustering algorithm from network theory. The second problem is to provide an alternative construction for the infinitesimal generator of a Markov process that respects statistical features over a large range of timescales. We demonstrate the methodology on three low-dimensional dynamical systems with stochastic and chaotic dynamics. We then apply the method to two high-dimensional dynamical systems, the Kuramoto-Sivashinky equations and data sampled from fluid-flow experiments via Particle-Image Velocimetry. We show that the methodology presented herein provides a robust reduced-order statistical representation of the underlying system. |
| title | Reduced Markovian Models of Dynamical Systems |
| topic | Chaotic Dynamics |
| url | https://arxiv.org/abs/2308.10864 |