Ab initio molecular dymamics (AIMD) simulation studies are a direct
way to visualize chemical reactions and help elucidate non-statistical dynamics that does not follow the intrinsic reaction coordinate. However,
due to the enormous amount of the ab initio energy gradient calculations
needed for AIMD, it has been largely restrained to limited sampling and
low level of theory (i.e., density functional theory with small basis sets).
To overcome this issue, a number of machine learning (ML) methods have
been employed to predict the energy gradient of the system of interest.
In this manuscript, we outline the theoretical foundations of a novel ML
method which trains from a varying set of atomic positions and their
energy gradients, called interpolating moving ridge regression (IMRR),
and directly predicts the energy gradient of a new set of atomic positions.
Several key theoretical findings are presented regarding the inputs used to
train IMRR and the predicted energy gradient. A hyperparameter used to
guide IMRR is rigorously examined as well. The method is then applied to
three bimolecular reactions studied with AIMD, including HBr+ + CO2,
H2S + CH, and C4H2 + CH, to demonstrate IMRR’s performance on different chemical systems of different sizes. This manuscript also compares
the computational cost of the energy gradient calculation with IMRR vs.
ab initio, and the results highlight IMRR as a viable option to greatly
increase the efficiency of AIMD.