Selectively enabling linear combination of atomic orbital coefficients to improve linear method optimizations in variational Monte Carlo

TL;DR

This paper introduces a selective approach to optimize atomic orbital coefficients in variational Monte Carlo, improving efficiency by removing unimportant parameters during the optimization process.

Contribution

The paper presents an expand-and-prune algorithm that dynamically removes unimportant orbital parameters to enhance the linear method's optimization in VMC.

Findings

Removing unimportant parameters improves optimization quality.

Large fractions of parameters can be safely pruned.

Pruning increases optimization efficacy in tested molecules.

Abstract

Second order stochastic optimization methods, such as the linear method, couple the updates of different parameters and, in so doing, allow statistical uncertainty in one parameter to affect the update of other parameters. In simple tests, we demonstrate that the presence of unimportant orbital optimization parameters, even when initialized to zero, seriously degrade the statistical quality of the linear method's update for important orbital parameters. To counteract this issue, we develop an expand-and-prune selective linear combination of atomic orbitals algorithm that removes unimportant parameters from the variational set on the fly. In variational Monte Carlo orbital optimizations in propene, butene, and pentadiene, we find that large fractions of the parameters can be safely removed, and that doing so can increase the efficacy of the overall optimization.