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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 multiparameter 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 semiautomated 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 an increase in speed by a factor 65. 

Context. Physical processes that govern the star and planet formation sequence influence the chemical composition and evolution of protoplanetary disks. Recent studies allude to an early start to planet formation already during the formation of a disk. To understand the chemical composition of protoplanets, we need to constrain the composition and structure of the disks from whence they are formed. Aims. We aim to determine the molecular abundance structure of the young disk around the TMC1A protostar on au scales in order to understand its chemical structure and any possible implications for disk formation. Methods. We present spatially resolved Atacama Large Millimeter/submillimeter Array observations of CO, HCO + , HCN, DCN, and SO line emission, as well as dust continuum emission, in the vicinity of TMC1A. Molecular column densities are estimated both under the assumption of optically thin emission from molecules in local thermodynamical equilibrium (LTE) as well as through more detailed non-LTE radiative transfer calculations. Results. Resolved dust continuum emission from the disk is detected between 220 and 260 GHz. Rotational transitions from HCO + , HCN, and SO are also detected from the inner 100 au region. We further report on upper limits to vibrational HCN υ 2 = 1, DCN, and N 2 D + lines. The HCO + emission appears to trace both the Keplerian disk and the surrounding infalling rotating envelope. HCN emission peaks toward the outflow cavity region connected with the CO disk wind and toward the red-shifted part of the Keplerian disk. From the derived HCO + abundance, we estimate the ionization fraction of the disk surface, and find values that imply that the accretion process is not driven by the magneto-rotational instability. The molecular abundances averaged over the TMC1A disk are similar to its protostellar envelope and other, older Class II disks. We meanwhile find a discrepancy between the young disk’s molecular abundances relative to Solar System objects. Conclusions. Abundance comparisons between the disk and its surrounding envelope for several molecular species reveal that the bulk of planet-forming material enters the disk unaltered. Differences in HCN and H 2 O molecular abundances between the disk around TMC1A, Class II disks, and Solar System objects trace the chemical evolution during disk and planet formation.