Data-driven stochastic representations of unresolved features in multiscale models (Q311083)

The authors report the results of a study where they investigate the use of sample data, generated by a fully resolved multiscale model, to construct stochastic representations of unresolved processes in reduced models. Three methods to model these stochastic representations are tested using the well-known Kac-Zwanzig heat bath model. These methods are: empirical distributions, conditional Markov chains, and conditional Ornstein-Uhlenbeck processes. They conclude that these methods reproduce the resolved model accurately. Furthermore, they show that the computational gain of this data-driven methodology can be substantial.NEWLINENEWLINEThe paper is organized in four sections and two appendices. In Section 1 the background and motivation for this study are presented. Section 2 describes the Kac-Zwanzig heat bath model. Section 3 is devoted to a rigorous and exhaustive exposition of the three strategies analyzed in the paper. In Section 4 the obtained results are discussed. The two appendices explain in detail the statistical techniques used in the study. This article is written with a remarkable rigor and precision.