A Tutorial Review of Bayesian Optimization with Gaussian Processes to Accelerate Stationary Point Searches

TL;DR

This paper reviews Bayesian optimization with Gaussian processes for accelerating stationary point searches on potential energy surfaces, unifying different search types within a common framework and providing practical extensions and code.

Contribution

It introduces a unified Bayesian optimization framework applicable to various stationary point searches, with practical extensions and a pedagogical Rust implementation.

Findings

Reduces electronic structure evaluations by about an order of magnitude.

Unified framework applies to minimization, saddle, and path searches.

Provides practical extensions like adaptive trust radius and scalable features.

Abstract

Building local surrogates to accelerate stationary point searches on potential energy surfaces spans decades of effort. Done correctly, surrogates can reduce the number of expensive electronic structure evaluations by roughly an order of magnitude while preserving the accuracy of the underlying theory, with the gain depending on oracle cost, search distance, and the availability of analytical forces. We present a unified Bayesian optimization view of minimization, single-point saddle searches, and double-ended path searches: all three share one six-step surrogate loop and differ only in the inner optimization target and the acquisition criterion. The framework uses Gaussian process regression with derivative observations, inverse-distance kernels, and active learning, and we develop optional extensions for production use, including farthest-point sampling with the Earth Mover's Distance, MAP regularization, an adaptive trust radius, and random Fourier features for scaling. Accompanying pedagogical Rust code demonstrates that all three applications use the same Bayesian optimization loop, bridging the gap between theoretical formulation and practical execution.