Model synthesis and identifiability analysis of stiff chemical reaction systems with inVAErt networks
For researchers in chemical kinetics and inverse problems, this work provides a novel method to handle non-identifiability in stiff systems, though it is an incremental application of existing inVAErt networks to a new domain.
The paper develops data-driven emulators for stiff chemical reaction systems and applies inVAErt networks to infer reaction rates, integration time, and initial conditions from species concentrations, achieving relative root mean squared errors of 10^{-5} to 10^{-3} across systems with 2-20 ODEs.
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.