Divergence-Kernel method for scores of random systems
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915373225345024 |
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| author | Ni, Angxiu |
| author_facet | Ni, Angxiu |
| contents | We derive the divergence-kernel formula for the scores of random dynamical systems, then formally pass to the continuous-time limit of SDEs. Our formula works for multiplicative noise systems over any period of time; it does not require hyperbolicity. We also consider several special cases: (1) for additive noise, we give a pure kernel formula; (2) for short-time, we give a pure divergence formula; (3) we give a formula which does not involve scores of the initial distribution. Based on the new formula, we derive a pathwise Monte-Carlo algorithm for scores, and demonstrate it on the 40-dimensional Lorenz 96 system with multiplicative noise. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04035 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Divergence-Kernel method for scores of random systems Ni, Angxiu Probability Numerical Analysis Dynamical Systems Optimization and Control 60H07, 60J60, 65D25, 65C30, 65C05 We derive the divergence-kernel formula for the scores of random dynamical systems, then formally pass to the continuous-time limit of SDEs. Our formula works for multiplicative noise systems over any period of time; it does not require hyperbolicity. We also consider several special cases: (1) for additive noise, we give a pure kernel formula; (2) for short-time, we give a pure divergence formula; (3) we give a formula which does not involve scores of the initial distribution. Based on the new formula, we derive a pathwise Monte-Carlo algorithm for scores, and demonstrate it on the 40-dimensional Lorenz 96 system with multiplicative noise. |
| title | Divergence-Kernel method for scores of random systems |
| topic | Probability Numerical Analysis Dynamical Systems Optimization and Control 60H07, 60J60, 65D25, 65C30, 65C05 |
| url | https://arxiv.org/abs/2507.04035 |