Machine Learning for Observables: Reactant to Product State Distributions for Atom-Diatom Collisions.

Machine learning- (ML) based models to predict product state distributions from a distribution of reactant conditions for atom-diatom collisions are presented and quantitatively tested. The models are based on function-, kernel- and grid-based representations of the reactant and product state distributions. All three methods predict final state distributions from explicit quasi-classical trajectory simulations with $R^2 > 0.998$. Although a function-based approach is found to be more than two times better in computational performance, the kernel- and grid-based approaches are preferred in terms of prediction accuracy, practicability and generality. For the function-based approach the choice of parametrized functions is crucial and this aspect is explicitly probed for final state vibrational distributions. Applications of the grid-based approach to non-equilibrium, multi-temperature initial state distributions are presented, a situation common to energy and state distributions in hypersonic flows. The role of such models in Direct Simulation Monte Carlo and computational fluid dynamics simulations is also discussed.