Predictive Mixing for Density Functional Theory (and other Fixed-Point Problems)

Density functional theory calculations use a significant fraction of current supercomputing time. The resources required scale with the problem size, internal workings of the code and the number of iterations to convergence, the latter being controlled by what is called mixing. This note describes a new approach to handling trust-regions within these and other fixed-point problems. Rather than adjusting the trust-region based upon improvement, the prior steps are used to estimate what they should be. Results are shown using both the Good and Bad Multisecant versions as well as Andersen and a hybrid approach. The predictive method works well, and is capable of adapting to different problem types particularly when coupled with the hybrid approach. It would be premature to claim that it is the best possible approach, but the results suggest that it may be; it is certainly better at choosing the right parameters than the author of this work.