Reducing the complexity of chemical networks via interpretable autoencoders

In many astrophysical applications, the cost of solving a chemical network represented by a system of ordinary differential equations (ODEs) grows significantly with the size of the network, and can often represent a significant computational bottleneck, particularly in coupled chemo-dynamical models. Although standard numerical techniques and complex solutions tailored to thermochemistry can somewhat reduce the cost, more recently, machine learning algorithms have begun to attack this challenge via data-driven dimensional reduction techniques. In this work, we present a new class of methods that take advantage of machine learning techniques to reduce complex data sets (autoencoders), the optimization of multi-parameter systems (standard backpropagation), and the robustness of well-established ODE solvers to to explicitly incorporate time-dependence. This new method allows us to find a compressed and simplified version of a large chemical network in a semi-automated fashion that can be solved with a standard ODE solver, while also enabling interpretability of the compressed, latent network. As a proof of concept, we tested the method on an astrophysically-relevant chemical network with 29 species and 224 reactions, obtaining a reduced but representative network with only 5 species and 12 reactions, and a x65 speed-up.
accepted A&A, code available at https://bitbucket.org/tgrassi/latent_ode_paper/