Ufmin: A Local Optimization Algorithm for Atomic Structures Using Machine Learning Potentials

Simulating atomic systems in their equilibrium configurations is necessary for accurately predicting relevant physical properties, and thus is a universal challenge in computational chemical engineering research. In essence, this process of determining geometry is a nonlinear optimization problem, and conventional methods rely on density-functional theory (DFT) to compute the energy and forces of the system at each step. DFT calculations yield highly accurate results but suffer from runtimes that scale poorly with the size of the system. Thus, reducing the number of force calls required could greatly increase computational efficiency. We present here a local optimization algorithm where the force minimization is performed on a surrogate model constructed from machine-learning (ML) interatomic potentials. The Ultra-Fast Force Fields (UF3) framework is used to construct these potentials using regularized linear regression and a basis set of cubic B-spline functions. We apply our algorithm, dubbed “UFMin”, to optimize the geometries of several perturbed bulk Pt structures and a perturbed heptamer island on Pt(111). A pairwise Morse potential is used as the reference potential in all cases. We find that for all bulk Pt systems tested, only three force calls are required to reduce the norm of the force to less than 1e-3 eV/A, significantly outperforming conventional methods that do not employ ML. Applying the same convergence criterion, only four force calls are required to optimize the heptamer island system. These encouraging results warrant further testing with UFMin, particularly on more complex systems and with more realistic reference potentials. We also discuss the possibility of using UFMin to accelerate nudged elastic band (NEB) calculations, which are commonly employed to identify transition state configurations and suffer from the same reliance on DFT as conventional geometry optimization.