Koopman operators and Extended Dynamic Mode Decomposition for a pair of forward and reverse chemical reactions which occur simultaneously

Abstract

We apply the Koopman operator theory and Extended Dynamic Mode Decomposition in a pair of forward and reverse chemical reactions which occur simultaneously with comparable speeds. The system of ODES which governs the evolution of the concentration of the reactants constitutes a nonlinear dynamical system with an interesting feature: It possesses uncountable infinite equilibria which reside on an algebraic surface. Koopman operator captures the dynamics of a nonlinear system, however it is infinite dimensional. In this study, we approximate the chemical reaction dynamics with a data-driven finite dimensional linear system which is defined on some augmented state space. We approximate so, with given initial conditions, the trajectories of the system and obtain an alternative description of the system based on Koopman operator theory, Extended Dynamic Mode Decomposition, and Machine Learning.