Non-Markovian Optimal Prediction
Numerical Analysis
2025-10-20 v1 Numerical Analysis
Abstract
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.
Cite
@article{arxiv.math/0101022,
title = {Non-Markovian Optimal Prediction},
author = {Alexandre J. Chorin and Ole H. Hald and Raz Kupferman},
journal= {arXiv preprint arXiv:math/0101022},
year = {2025}
}
Comments
17 pages, includes 1 figure