Model synthesis and identifiability analysis of stiff chemical reaction systems with inVAErt networks

TL;DR

This paper develops efficient data-driven emulators and an inverse modeling framework for stiff chemical reaction systems, enabling accurate parameter inference and identifiability analysis across various complex kinetics.

Contribution

It introduces the use of inVAErt networks for inverse problems in chemical kinetics, addressing ill-posedness and demonstrating effectiveness on diverse systems.

Findings

Emulators achieve relative RMSE from 10^{-5} to 10^{-3}.

Manifolds of non-identifiable rates are consistent with local analysis.

Framework applies to systems with up to 20 differential equations and 25 parameters.

Abstract

We consider the problem of learning data-driven replicas for stiff systems of ordinary differential equations arising in chemical kinetics that can be evaluated with high computational efficiency. We first focus on training emulators for families of reaction equations under varying reaction rates, using conditional residual networks or long-short term memory architectures. We then apply a recently proposed data-driven framework known as ``inVAErt networks'' to address the ill-posed inverse problem of inferring reaction rates, integration time, and possibly initial conditions from a target set of species concentrations - a problem that has received relatively little attention in the literature. The proposed approach is demonstrated on chemical systems with reversible and irreversible kinetics, spanning 2 to 20 differential equations, 3 to 20 chemical species, and 3 to 25 reaction rate parameters. Relative root mean squared errors produced by the proposed emulators range from $10^{-5}$ for lower-dimensional systems to $10^{-4}$ and $10^{-3}$ for an air pollution model and a hydrogen-air reaction system, respectively. Manifolds of non-identifiable reaction rates recovered by the proposed approach can be analytically verified for simple systems and are consistent with local identifiability analysis in higher dimensions.