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| Autors principals: | , , |
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| Format: | Preprint |
| Publicat: |
2001
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| Matèries: | |
| Accés en línia: | https://arxiv.org/abs/math/0101022 |
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| _version_ | 1866911217144037376 |
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| author | Chorin, Alexandre J. Hald, Ole H. Kupferman, Raz |
| author_facet | Chorin, Alexandre J. Hald, Ole H. Kupferman, Raz |
| contents | Optimal prediction methods compensate for a lack of resolution in the numerical solution of complex problems through the use of prior statistical information. We know from previous work that in the presence of strong underresolution a good approximation needs a non-Markovian "memory", determined by an equation for the "orthogonal", i.e., unresolved, dynamics. We present a simple approximation of the orthogonal dynamics, which involves an ansatz and a Monte-Carlo evaluation of autocorrelations. The analysis provides a new understanding of the fluctuation-dissipation formulas of statistical physics. An example is given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0101022 |
| institution | arXiv |
| publishDate | 2001 |
| record_format | arxiv |
| spellingShingle | Non-Markovian Optimal Prediction Chorin, Alexandre J. Hald, Ole H. Kupferman, Raz Numerical Analysis Optimal prediction methods compensate for a lack of resolution in the numerical solution of complex problems through the use of prior statistical information. We know from previous work that in the presence of strong underresolution a good approximation needs a non-Markovian "memory", determined by an equation for the "orthogonal", i.e., unresolved, dynamics. We present a simple approximation of the orthogonal dynamics, which involves an ansatz and a Monte-Carlo evaluation of autocorrelations. The analysis provides a new understanding of the fluctuation-dissipation formulas of statistical physics. An example is given. |
| title | Non-Markovian Optimal Prediction |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/math/0101022 |