In this study, we investigate how to use sample data, generated by a fully resolved multiscale model, to construct stochastic representations of unresolved scales in reduced models. We explore three methods to model these stochastic representations. They employ empirical distributions, conditional Markov chains, and conditioned Ornstein–Uhlenbeck processes, respectively. The Kac–Zwanzig heat bath model is used as a prototype model to illustrate the methods. We demonstrate that all tested strategies reproduce the dynamics of the resolved model variables accurately. Furthermore, we show that the computational cost of the reduced model is several orders of magnitude lower than that of the fully resolved model.

Additional Metadata
THEME Null option (theme 11)
Journal Communications in Mathematical Sciences
Grant This work was funded by the The Netherlands Organisation for Scientific Research (NWO); grant id nwo/639.072.207 - Stochastic models for unresolved scales in geophysical flows
Citation
Verheul, N, & Crommelin, D.T. (2016). Data-driven stochastic representations of unresolved features in multiscale models. Communications in Mathematical Sciences, 14(5), 1213–1236.