Bayesian Optimization with Gaussian Processes to Accelerate Stationary Point Searches

2026-03-11

AI Summary

This work addresses the high computational cost of quantum chemical calculations in locating stationary points—minima and saddle points—on potential energy surfaces by proposing a unified six-step Bayesian optimization framework. The approach integrates Gaussian process surrogate models capable of incorporating derivative observations, optimal transport theory, and active learning, and introduces several innovations: farthest-point sampling based on Earth Mover’s Distance, variance-barrier MAP regularization, oscillation detection, and an adaptive trust radius. To enhance scalability in high-dimensional settings, stochastic Fourier features are employed to decouple hyperparameter training. Experimental results demonstrate that the method reduces the number of required energy evaluations by nearly an order of magnitude while preserving theoretical accuracy, and its generality and practicality across diverse tasks are validated through a unified implementation in Rust.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Optimization

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Accelerating the explorations of stationary points on potential energy surfaces building local surrogates spans decades of effort. Done correctly, surrogates reduce required evaluations by an order of magnitude while preserving the accuracy of the underlying theory. We present a unified Bayesian Optimization view of minimization, single point saddle searches, and double ended saddle searches through a unified six-step surrogate loop, differing only in the inner optimization target and acquisition criterion. The framework uses Gaussian process regression with derivative observations, inverse-distance kernels, and active learning. The Optimal Transport GP extensions of farthest point sampling with Earth mover's distance, MAP regularization via variance barrier and oscillation detection, and adaptive trust radius form concrete extensions of the same basic methodology, improving accuracy and efficiency. We also demonstrate random Fourier features decouple hyperparameter training from predictions enabling favorable scaling for high-dimensional systems. Accompanying pedagogical Rust code demonstrates that all applications use the exact same Bayesian optimization loop, bridging the gap between theoretical formulation and practical execution.

Problem

• Bayesian Optimization
• Stationary Point Search
• Potential Energy Surface
• Gaussian Processes
• Surrogate Modeling

Innovation

• Bayesian Optimization
• Gaussian Processes
• Stationary Point Search
• Optimal Transport
• Random Fourier Features