Stochastic Modeling of Unresolved Scales in Complex Systems

TL;DR

This paper introduces a stochastic modeling approach to account for unresolved scales in complex multiscale systems, improving the accuracy of simulations where certain mechanisms are not explicitly represented.

Contribution

It proposes a novel stochastic scheme for parameterizing unresolved scales in nonlinear PDE models of complex systems.

Findings

The stochastic scheme effectively captures the impact of unresolved scales.

Application to an example demonstrates improved modeling accuracy.

The approach provides a framework for handling uncertainties in multiscale simulations.

Abstract

Model uncertainties and simulation uncertainties occur in mathematical modeling of multiscale complex systems, since some mechanisms or scales are not represented (i.e., "unresolved") due to lack in our understanding of these mechanisms or limitations in computational power. The impact of these unresolved scales on the resolved scales needs to be parameterized or taken into account. A stochastic scheme is devised to take the effects of unresolved scales into account, in the context of solving nonlinear partial differential equations. An example is presented to demonstrate this strategy.