A structural optimization algorithm with stochastic forces and stresses

We propose an algorithm for optimizations in which the gradients contain stochastic noise. This arises, for example, in structural optimizations when computations of forces and stresses rely on methods involving Monte Carlo sampling, such as quantum Monte Carlo or neural network states, or are performed on quantum devices that have intrinsic noise. Our proposed algorithm is based on the combination of two ingredients: an update rule derived from the steepest-descent method, and a staged scheduling of the targeted statistical error and step size, with position averaging. We compare it with commonly applied algorithms, including some of the latest machine learning optimization methods, and show that the algorithm consistently performs efficiently and robustly under realistic conditions. Applying this algorithm, we achieve full-degree optimizations in solids using ab initio many-body computations, by auxiliary-field quantum Monte Carlo with plane waves and pseudopotentials. A potential metastable structure in Si is discovered using density-functional calculations with synthetic noisy forces.