Accelerating Fourth-Generation Machine Learning Potentials Using Quasi-Linear Scaling Particle Mesh Charge Equilibration
Moritz Gubler, Jonas A. Finkler, Moritz R. Schäfer, Jörg Behler, Stefan Goedecker
Abstract
Machine learning potentials (MLPs) have revolutionized the field of atomistic simulations by describing atomic interactions with the accuracy of electronic structure methods at a small fraction of the cost. Most current MLPs construct the energy of a system as a sum of atomic energies, which depend on information about the atomic environments provided in the form of predefined or learnable feature vectors. If, in addition, nonlocal phenomena like long-range charge transfer are important, fourth-generation MLPs need to be used, which include a charge equilibration (Qeq) step to take the global structure of the system into account. This Qeq can significantly increase the computational cost and thus can become a computational bottleneck for large systems. In this Article, we present a highly efficient formulation of Qeq that does not require the explicit computation of the Coulomb matrix elements, resulting in a quasi-linear scaling method. Moreover, our approach also allows for the efficient calculation of energy derivatives, which explicitly consider the global structure-dependence of the atomic charges as obtained from Qeq. Due to its generality, the method is not restricted to MLPs and can also be applied within a variety of other force fields.