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

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.