Predicted state-to-state collisional rate coefficients from neural networks

Abstract

Molecular spectra observed in the interstellar medium are commonly analyzed using non-local thermodynamic equilibrium models, which requires accurate state-to-state collisional rate coefficients. Close-coupling calculations become prohibitively expensive for transitions from highly excited rotational states, therefore available datasets are often truncated at low initial states and temperatures; and since each new system also requires an accurate ab initio potential energy surface, many detected molecules have no collisional data. We employ two machine learning strategies to predict rotational state-to-state rate coefficients of molecules included in the train set beyond the range of initial states and temperatures computed so far, and predicting those of a molecule absent from training and validation sets. Feed-forward neural networks are trained on state-to-state de-excitation rate coefficients of 24 linear molecules colliding with para-H2. Scheme 1 includes all systems in the train+validation set, with 70%, 80%, and 90% initial-state boundaries and a 90% temperature boundary. Scheme 2 is trained on 22 systems described only by transition and molecular properties, and predicts two excluded systems, CS and CF+, whose astrophysical impact is explored with non-LTE calculations. For the 90% boundary, Scheme 1 predicts 99.4% of the test transitions within a factor of 2, and no prediction deviates from the reference value by more than a factor of 4.7. This model was used to complete 18 datasets. Scheme 2 reproduces the rate coefficients of two excluded systems within a factor of 3 for more than 92% of their transitions. Both schemes provide near-instantaneous complements to close-coupling calculations: Scheme 1 extends the range of a molecule already included in the training set with high accuracy, while Scheme 2 gives a reasonable first estimate for a molecule that has not been studied.