Acceleration of Moment Bound Optimization for Stochastic Chemical Reactions Using Reaction-wise Sparsity of Moment Equations

TL;DR

This paper introduces a sparsity-exploiting matrix decomposition technique to accelerate semidefinite programming for bounding moments in stochastic chemical kinetics, addressing computational challenges.

Contribution

It develops a novel method leveraging reaction-wise sparsity to decompose semidefinite constraints, significantly reducing computational costs in moment bounding problems.

Findings

The method reduces the size of semidefinite constraints.

It maintains accurate bounds while improving computational efficiency.

Applicable to large-scale stochastic chemical reaction networks.

Abstract

Moment dynamics in stochastic chemical kinetics often involve an infinite chain of coupled equations, where lower-order moments depend on higher-order ones, making them analytically intractable. Moment bounding via semidefinite programming provides guaranteed upper and lower bounds on stationary moments. However, this formulation suffers from the rapidly growing size of semidefinite constraints due to the combinatorial growth of moments with the number of molecular species. In this paper, we propose a sparsity-exploiting matrix decomposition method for semidefinite constraints in stationary moment bounding problems to reduce the computational cost of the resulting semidefinite programs. Specifically, we characterize the sparsity structure of moment equations, where each reaction involves only a subset of variables determined by its reactants, and exploit this structure to decompose the semidefinite constraints into smaller ones. We demonstrate that the resulting formulation reduces the computational cost of the optimization problem while providing practically useful bounds.