Stabilized Quasi-Newton Optimization of Noisy Potential Energy Surfaces

TL;DR

This paper introduces stabilized quasi-Newton methods for optimizing noisy potential energy surfaces, improving the reliability and efficiency of atomic position optimizations in electronic structure calculations.

Contribution

The authors develop a stabilized quasi-Newton approach that effectively handles computational noise, enhancing optimization stability and performance in electronic structure tasks.

Findings

The new methods outperform existing optimization algorithms in benchmarks.

Stabilized quasi-Newton techniques improve reliability in noisy environments.

The approach is applicable to both minimization and saddle point searches.

Abstract

Optimizations of atomic positions belong to the most commonly performed tasks in electronic structure calculations. Many simulations like global minimum searches or characterizations of chemical reactions require performing hundreds or thousands of minimizations or saddle computations. To automatize these tasks, optimization algorithms must not only be efficient, but also very reliable. Unfortunately computational noise in forces and energies is inherent to electronic structure codes. This computational noise poses a sever problem to the stability of efficient optimization methods like the limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm. We here present a technique that allows obtaining significant curvature information of noisy potential energy surfaces. We use this technique to construct both, a stabilized quasi-Newton minimization method and a stabilized quasi-Newton saddle finding approach. We demonstrate with the help of benchmarks that both the minimizer and the saddle finding approach are superior to comparable existing methods.