Data-Driven Stochastic Multiscale Method

A Multiscale Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficients

In this paper, we propose a multiscale data-driven stochastic method (MsDSM) to study stochastic partial differential equations (SPDEs) in the multiquery setting. This method combines the advantages of the recently developed multiscale model reduction method [M. L. Ci, T. Y. Hou, and Z. Shi, ESAIM Math. Model. Numer. Anal., 48 (2014), pp. 449–474] and the datadriven stochastic method (DSM) [M. ...

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Modeling diffusion in random heterogeneous media: Data-driven models, stochastic collocation and the variational multiscale method

In recent years, there has been intense interest in understanding various physical phenomena in random heterogeneous media. Any accurate description/simulation of a process in such media has to satisfactorily account for the twin issues of randomness as well as the multi-length scale variations in the material properties. An accurate model of the material property variation in the system is an ...

Modeling multiscale diffusion processes in random heterogeneous media

A simple stochastic up-scaling strategy is presented for incorporating the effects of micro-scale variations of thermal conductivity in the thermal analysis of macro-scale systems. Incomplete characterization of the fine-scale variation necessitates posing the thermal conductivity as a stochastic multiscale random field. A data-driven approach coupled with a non-linear dimension reduction algor...

AN INFORMATION-THEORETIC MULTISCALE FRAMEWORK WITH APPLICATIONS TO POLYCRYSTALLINE MATERIALS AFOSR GRANT NUMBER FA9550-07-1-0139 Prof

The effect of diverse sources of uncertainties and the intrinsically multi-scale nature of real-world physical systems poses a considerable challenge to analyze such systems. Such phenomena are particularly critical in material systems wherein microstructural variability and randomness at lower scales have a significant impact on the behavior of the system. Towards this goal, some of our accomp...

Parallel in Time Simulation of Multiscale Stochastic Chemical Kinetics

A version of the time-parallel algorithm parareal is analyzed and applied to stochastic models in chemical kinetics. A fast predictor at the macroscopic scale (evaluated in serial) is available in the form of the usual reaction rate equations. A stochastic simulation algorithm is used to obtain an exact realization of the process at the mesoscopic scale (in parallel). The underlying stochastic ...