Exhaustive state-to-state cross sections for reactive molecular collisions from importance sampling simulation and a neural network representation

High-temperature, reactive gas flow is inherently nonequilibrium in terms of energy and state population distributions. Modeling such conditions is challenging even for the smallest molecular systems due to the extremely large number of accessible states and transitions between them. Here, neural networks (NNs) trained on explicitly simulated data are constructed and shown to provide quantitatively realistic descriptions which can be used in mesoscale simulation approaches such as Direct Simulation Monte Carlo to model gas flow at the hypersonic regime. As an example, the state-to-state cross sections for N(4S) + NO(2Π) → O(3P) + N2(X1Σ+g ) are computed from quasiclassical trajectory (QCT) simulations. By training NNs on a sparsely sampled noisy set of state-to-state cross sections, it is demonstrated that independently generated reference data are predicted with high accuracy. State-specific and total reaction rates as a function of temperature from the NN are in quantitative agreement with explicit QCT simulations and confirm earlier simulations, and the final state distributions of the vibrational and rotational energies agree as well. Thus, NNs trained on physical reference data can provide a viable alternative to computationally demanding explicit evaluation of the microscopic information at run time. This will considerably advance the ability to realistically model nonequilibrium ensembles for network-based simulations. Support from the Swiss National Science Foundation through Grant No. 200021-117810, the NCCR MUST (to M.M.), and the University of Basel is also acknowledged. Part of this work was supported by the United State Department of the Air Force which is gratefully acknowledged (to M.M.). The codes for training the NN-model and computing the cross sections from the NN-model are freely available from https://github.com/MeuwlyGroup/NNcross together with a sample training data set