Gaussian process based optimization of molecules and solids using noisy energy surfaces from Quantum Monte Carlo

Optimization of atomic coordinates and lattice parameters remains a significant challenge to the wide use of stochastic electronic structure methods such as quantum Monte Carlo. Measurements of the forces and stress tensor by these methods contain statistical errors, challenging conventional numerical optimization methods that assume deterministic results. Additionally, gradients are expensive to compute to very high statistical accuracy near an energy minima, where the energy surfaces are flat. Furthermore, gradients are not yet available for some methods. Here, we explore the use of Gaussian process based techniques to sample the energy surfaces and reduce sensitivity to the statistical nature of the problem. We apply these methods to non-trivial but still low dimensional problems such as simple molecules and bulk solids. Compared to traditionally applied methods, they are able to converge faster when the surfaces are not quadratic and the statistical sampling of the energy surfaces can be performed rapidly in parallel.