Marginal process framework: A model reduction tool for Markov jump processes

TL;DR

This paper introduces a new model reduction framework for Markov jump processes, enabling simplified analysis of complex coupled systems, with applications demonstrated on exclusion processes and reaction networks.

Contribution

It extends the marginal process framework to fully coupled Markov jump processes using entropic matching for finite-dimensional approximation.

Findings

Effective reduction of Markov jump process models.

Application to exclusion process and reaction networks.

Analytical and numerical validation of the approximation.

Abstract

Markov jump process models have many applications across science. Often, these models are defined on a state-space of product form and only one of the components of the process is of direct interest. In this paper, we extend the marginal process framework, which provides a marginal description of the component of interest, to the case of fully coupled processes. We use entropic matching to obtain a finite-dimensional approximation of the filtering equation, which governs the transition rates of the marginal process. The resulting equations can be seen as a combination of two projection operations applied to the full master equation, so that we obtain a principled model reduction framework. We demonstrate the resulting reduced description on the totally asymmetric exclusion process. An important class of Markov jump processes are stochastic reaction networks, which have applications in chemical and biomolecular kinetics, ecological models and models of social networks. We obtain a particularly simple instantiation of the marginal process framework for mass-action systems by using product-Poisson distributions for the approximate solution of the filtering equation. We investigate the resulting approximate marginal process analytically and numerically.