On Projection-Based Model Reduction of Biochemical Networks-- Part I: The Deterministic Case

TL;DR

This paper introduces a projection-based model reduction method for biochemical networks that preserves stability, positivity, and structure, offering two algorithms with different accuracy and simplicity, demonstrated through numerical examples.

Contribution

It proposes a novel reduction algorithm using generalized block diagonal Gramians to maintain key properties of biochemical network models.

Findings

The method effectively preserves stability and positivity.

Two algorithms balance accuracy and ease of simulation.

Numerical examples validate the approach.

Abstract

This paper addresses the problem of model reduction for dynamical system models that describe biochemical reaction networks. Inherent in such models are properties such as stability, positivity and network structure. Ideally these properties should be preserved by model reduction procedures, although traditional projection based approaches struggle to do this. We propose a projection based model reduction algorithm which uses generalised block diagonal Gramians to preserve structure and positivity. Two algorithms are presented, one provides more accurate reduced order models, the second provides easier to simulate reduced order models. The results are illustrated through numerical examples.