Genetic programming-based learning of carbon interatomic potential for materials discovery

Abstract: Efficient and accurate interatomic potential functions are critical to computational study of materials while searching for structures with desired properties. Traditionally, potential functions or energy landscapes are designed by experts based on theoretical or heuristic knowledge. Here, we propose a new approach to leverage strongly typed parallel genetic programming (GP) for potential function discovery. We use a multi-objective evolutionary algorithm with NSGA-III selection to optimize individual age, fitness, and complexity through symbolic regression. With a DFT dataset of 863 unique carbon allotrope configurations drawn from 858 carbon structures, the generated potentials are able to predict total energies within $\pm 7.70$ eV at low computational cost while generalizing well across multiple carbon structures. Our code is open source and available at \url{http://www.github.com/usccolumbia/mlpotential