Extrapolating Collisional Rate Coefficients for Molecules of Astrophysical Interest Using Neural Networks

Abstract

State-to-state rate coefficients for inelastic molecular collisions are essential inputs for non-local thermodynamic equilibrium radiative transfer models, yet their computation using quantum scattering methods is prohibitive for large molecules and highly excited rotational states. We investigate the ability of artificial neural networks to extend existing datasets of collisional excitation rate coefficients without performing additional scattering calculations. A multilayer perceptron model was trained using molecular quantum numbers, level energies, energy gaps, and kinetic temperature as descriptors, and optimized on logarithmic rate coefficients. The model was tested on diverse collision systems ranging from simple diatomic molecules (CO, SiO) to open-shell species (SO), small asymmetric tops (H$_2$O, SO$_2$), and complex organic molecules (benzonitrile and vinyl cyanide) colliding with H$_2$ molecules or He atoms. Extrapolations were performed toward higher rotational levels, higher temperatures, and combinations of both. For most systems, predictions of rate coefficients involving previously unseen rotational states yielded mean error factors between 1.1 and 1.5, with the dominant rate coefficients generally reproduced more accurately than weaker transitions. Temperature extrapolations proved particularly successful, while combined extrapolations in temperature and rotational levels remained accurate to within a factor of two in most cases. The prediction quality depends on the interplay between dataset size, temperature range, molecular complexity, and the presence of clear collisional propensity rules. Overall, the approach demonstrates that machine learning can provide a practical route to extending collisional datasets for astrophysical applications, especially for large molecules for which additional quantum-scattering calculations are computationally demanding.