Interstellar collision rates without fresh quantum scattering: neural networks fill 18 systems to 500 K and guess unseen CS and CF+

Non-LTE analysis of interstellar molecular spectra needs state-to-state collisional rate coefficients, and such data exist for only about one-third of the 350 molecules detected so far in the interstellar medium or circumstellar shells, usually truncated at low initial states and temperatures. Rate coefficients are traditionally obtained from close-coupling quantum dynamics, which grows expensive as the initial rotational state rises because higher states need a larger rotational basis set, so many systems have data only for the first rotational states and low temperatures. On de-excitation rate coefficients for 24 linear molecules colliding with para-H2 taken from the BASECOL database, a 90% initial-state boundary predicts 99.4% of test transitions within a factor of 2, with an RMSE of 0.07 and no prediction off by more than a factor of 4.7.

Two schemes cover two kinds of gap: one pushes a molecule already in the training set toward higher initial states and temperatures, the other estimates a molecule never computed before from molecular properties alone. Earlier machine-learning work mostly filled gaps in systems that already had scattering calculations or improved the accuracy of approximate calculations, and it needed a potential energy surface or partial scattering information for the target. Scheme 1 trains ten networks on low initial-state, low-temperature data and completes the datasets of 18 systems up to 500 K and initial-state energies of 696 cm-1; Scheme 2 trains on 22 systems and reproduces 99.47% of the transitions of the fully excluded CF+ and 92.05% of those of CS within a factor of 3.

The models target rotational collisions of linear molecules with para-H2, with training data drawn from the BASECOL database; Scheme 1 completes 18 systems up to 500 K and initial-state energies of 696 cm-1 at the 90% boundary, and Scheme 2 gives a first estimate for CS and CF+. The Scheme 2 predictions were fed into RADEX under a uniform sphere geometry, a background temperature of 2.73 K, and fixed column density and line width to compute line ratios for a density diagnostic. The authors propose extending the approach to other colliders and target types as a natural continuation.

Scheme 2 is restricted to linear molecules colliding with para-H2, and its system-describing features take only 22 distinct combinations, so extrapolation to molecules far from the covered feature space remains untested. The rate coefficients of CS span roughly four orders of magnitude more than those of CF+, so a larger fraction of its transitions lies in the small-rate regime where training data are sparsest, and the better CF+ performance should be read with that caveat. The Scheme 2 deviation in RADEX varies with the system, and the authors position it as a reasonable first estimate.