Koopman Operator Inference for the Chemical Master Equation

Abstract

We infer kinetic rates of stochastic reaction networks from molecular-state pairs separated by a fixed time lag, without constructing the large state space of the Chemical Master Equation. Extended dynamic mode decomposition estimates the finite-time evolution of selected functions of the molecular state. A matrix logarithm then gives a projected generator whose species rows determine the rates through the known reaction stoichiometry. A finite set of functions introduces a systematic bias. We construct additional functions from the reaction channels and prove that each level of closure moves the first bias term to higher order. Spectral formulas identify the omitted modes responsible for this bias and show when the logarithm amplifies sampling error. Exact calculations and experiments on five reaction networks confirm the predicted error behavior and show when the added functions improve finite-sample rate recovery.