On Moment Matching for Stochastic Systems

TL;DR

This paper explores model reduction for stochastic systems via moment matching, introducing new classes of reduced models that balance approximation accuracy with computational feasibility.

Contribution

It characterizes stochastic moments, proposes relaxed matching methods, and develops computationally tractable reduced-order models for stochastic differential equations.

Findings

Identifies the stochastic generalization of moments.

Proposes two relaxed moment matching approaches.

Develops reduced models with feasible computational costs.

Abstract

In this paper we study the problem of model reduction by moment matching for stochastic systems. We characterize the mathematical object which generalizes the notion of moment to stochastic differential equations and we find a class of models which achieve moment matching. However, differently from the deterministic case, these reduced-order models cannot be considered "simpler" because of the high computational cost paid to determine the moment. To overcome this difficulty, we relax the moment matching problem in two different ways and we present two classes of reduced-order models which, approximately matching the stochastic moment, are computationally tractable.