A structural optimization algorithm with stochastic forces and stresses.

Area of Science:

• Computational Physics
• Materials Science
• Quantum Computing

Background:

• Structural optimizations often involve stochastic noise from methods like Monte Carlo sampling or quantum device imperfections.
• Existing optimization algorithms struggle with the inherent noise in these computations, limiting accuracy and efficiency.

Purpose of the Study:

• To develop a robust and efficient optimization algorithm for systems with noisy gradients.
• To demonstrate the algorithm's effectiveness in ab initio many-body computations and materials discovery.

Main Methods:

• A novel algorithm combining a steepest-descent update rule with staged scheduling of statistical error and step size.
• Position averaging techniques to mitigate the effects of stochastic noise.
• Comparison with established and state-of-the-art machine learning optimization methods.

Main Results:

• The proposed algorithm demonstrates consistent efficiency and robustness under realistic noisy conditions.
• Successful application to full-degree optimizations in solids using ab initio many-body computations (auxiliary-field quantum Monte Carlo).
• Discovery of a potential metastable structure in Silicon using density-functional calculations with synthetic noisy forces.

Conclusions:

• The new algorithm effectively addresses challenges posed by stochastic noise in scientific optimizations.
• It enables accurate and efficient large-scale computations, advancing fields like materials science and quantum computing.
• The method facilitates the discovery of novel material structures and properties.