A new framework for extracting coarse-grained models from time series with multiscale structure

JOURNAL OF COMPUTATIONAL PHYSICS

卷:296

Article

Kalliadasis, S.¹  Krumscheid, S.²  Pavliotis, G. A.² 

[1] Univ London Imperial Coll Sci Technol & Med, Dept Chem Engn, London SW7 2AZ, England

[2] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England

关键词: Parametric inference;    Stochastic differential equations;    Multiscale diffusion;    Chaotic dynamics;    Homogenization;    Coarse-graining;   

DOI  :  10.1016/j.jcp.2015.05.002

来源: Elsevier

【 摘 要 】

In many applications it is desirable to infer coarse-grained models from observational data. The observed process often corresponds only to a few selected degrees of freedom of a high-dimensional dynamical system with multiple time scales. In this work we consider the inference problem of identifying an appropriate coarse-grained model from a single time series of a multiscale system. It is known that estimators such as the maximum likelihood estimator or the quadratic variation of the path estimator can be strongly biased in this setting. Here we present a novel parametric inference methodology for problems with linear parameter dependency that does not suffer from this drawback. Furthermore, we demonstrate through a wide spectrum of examples that our methodology can be used to derive appropriate coarse-grained models from time series of partial observations of a multiscale system in an effective and systematic fashion. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free