Parsimonious Potential Energy Surface Expansions Using Dictionary Learning with Multipass Greedy Selection

Potential energy surfaces fit with basis set expansions have been shown to provide accurate representations of electronic energies and have enabled a variety of high-accuracy dynamics, kinetics, and spectroscopy applications. The number of terms in these expansions scales poorly with system size, a drawback that challenges their use for systems with more than ∼10 atoms. A solution is presented here using dictionary learning. Subsets of the full set of conventional basis functions are optimized using a newly developed multipass greedy regression method inspired by forward and backward selection methods from the statistics, signal processing, and machine learning literatures. The optimized representations have accuracies comparable to the full set but are 1 or more orders of magnitude smaller, and notably, the number of terms in the optimized multipass greedy expansions scales approximately linearly with the number of atoms.