An efficient data-driven solver for Fokker-Planck equations: algorithm and analysis
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2019
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| _version_ | 1866913509983387648 |
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| author | Dobson, Matthew Li, Yao Zhai, Jiayu |
| author_facet | Dobson, Matthew Li, Yao Zhai, Jiayu |
| contents | Computing the invariant probability measure of a randomly perturbed dynamical system usually means solving the stationary Fokker-Planck equation. This paper studies several key properties of a novel data-driven solver for low-dimensional Fokker-Planck equations proposed in [15]. Based on these results, we propose a new `block solver' for the stationary Fokker-Planck equation, which significantly improves the performance of the original algorithm. Some possible ways of reducing numerical artifacts caused by the block solver are discussed and tested with examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1906_02600 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | An efficient data-driven solver for Fokker-Planck equations: algorithm and analysis Dobson, Matthew Li, Yao Zhai, Jiayu Numerical Analysis Dynamical Systems 65N99, 65C05, 37M25 Computing the invariant probability measure of a randomly perturbed dynamical system usually means solving the stationary Fokker-Planck equation. This paper studies several key properties of a novel data-driven solver for low-dimensional Fokker-Planck equations proposed in [15]. Based on these results, we propose a new `block solver' for the stationary Fokker-Planck equation, which significantly improves the performance of the original algorithm. Some possible ways of reducing numerical artifacts caused by the block solver are discussed and tested with examples. |
| title | An efficient data-driven solver for Fokker-Planck equations: algorithm and analysis |
| topic | Numerical Analysis Dynamical Systems 65N99, 65C05, 37M25 |
| url | https://arxiv.org/abs/1906.02600 |