Kron Reduction in Species-Reaction Graphs of Mass-Action Chemical Reaction Networks

We propose a novel approach for model reduction in kinetic models of mass-action chemical reaction networks(CRN), based on the Kron reduction of the species-reaction graph associated with the network. This type of reduction comes from the theory of linear electrical networks. Although CRNs are not linear, they are endowed with a linear structure defined by the graph Laplacian, describing how the information propagates in the network. We show how to define a graph Laplacian for the species-reaction graph, by assigning appropriate weights to the edges of this graph. We use the Laplacian to rewrite the chemical kinetics of the CRN as a hybrid differential-algebraic system. We show that the Kron reduction preserves the hybrid structure and transforms the Laplacian into the Schur complement of the original one. The entire procedure is automated through a user-friendly Python package. We validate the applicability of this reduction technique using a real-world example of a CRN and demonstrate its effectiveness in practical scenarios.