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

arXiv: https://arxiv.org/abs/2603.10992 · HTML: https://mlsanity.com/paper/2603.10992/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 79 references that are in the map.
- First posted on arXiv 11 Mar 2026.

## Builds on (most cited first, 12 of 12)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Transition1x -- a Dataset for Building Generalizable Reactive Machine Learning Potentials](https://mlsanity.com/paper/2207.12858/) (2022)
- [AiiDA: Automated Interactive Infrastructure and Database for Computational Science](https://mlsanity.com/paper/1504.01163/) (2015)
- [Pushing the limits of unconstrained machine-learned interatomic potentials](https://mlsanity.com/paper/2601.16195/) (2026)
- [Nudged elastic band calculations accelerated with Gaussian process regression](https://mlsanity.com/paper/1706.04606/) (2017)
- [Algorithmic Differentiation for Automated Modeling of Machine Learned Force Fields](https://mlsanity.com/paper/2208.12104/) (2022)
- [Wigner kernels: body-ordered equivariant machine learning without a basis](https://mlsanity.com/paper/2303.04124/) (2023)
- [IRA: A shape matching approach for recognition and comparison of generic atomic patterns](https://mlsanity.com/paper/2111.00939/) (2021)
- [Efficient Implementation of Gaussian Process Regression Accelerated Saddle Point Searches with Application to Molecular Reactions](https://mlsanity.com/paper/2505.12519/) (2025)
- [Sliced gradient-enhanced Kriging for high-dimensional function approximation](https://mlsanity.com/paper/2204.03562/) (2022)
- [Adaptive Pruning for Increased Robustness and Reduced Computational Overhead in Gaussian Process Accelerated Saddle Point Searches](https://mlsanity.com/paper/2510.06030/) (2025)
- [Two-dimensional RMSD projections for reaction path visualization and validation](https://mlsanity.com/paper/2512.07329/) (2025)

## Abstract (arXiv)

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.