Finding New Mixing Strategies for Self Consistent Field Procedures Using Reinforcement Learning

Density mixing is a technique to improve the convergence for self-consistent field (SCF) procedures, and is used extensively to calculate electronic structure and transport properties in the context of density functional theory (DFT). Typically, a single mixing method will be chosen for the whole of a SCF calculation, but recent research suggests that alternating the mixing strategy between subsequent SCF iterations can improve the time of convergence. There are many untested SCF mixing methods beyond those already discovered that can be constructed using combinations of established methods. We present a new method to discover mixing strategies by applying a reinforcement learning algorithm (RLA). The state space of the RLA consists of SCF parameters such as the density, potential and convergence error. The action space of the RLA consists of previously developed mixing methods including simple mixing, Broyden mixing and Pulay mixing, with the crucial point being that the RLA is able to alter the mixing strategy in situ.