Bayesian Optimization with Gaussian Processes to Accelerate Stationary Point Searches
2026-03-11 • Machine Learning
Machine Learning
AI summaryⓘ
The authors present a new way to find important points on energy surfaces, like tiny maps of how molecules behave, using a single smart process called Bayesian Optimization. This method uses a statistical model called Gaussian processes with tricks like looking at rates of change and smart sampling to make the search faster and just as accurate. Their approach works the same way whether they are trying to find the lowest energy point or specific saddle points crucial for reactions. They also provide example code to show how the method can be easily used in practice. Overall, the work combines several advanced techniques to make exploring energy landscapes more efficient and reliable.
Bayesian OptimizationGaussian Process RegressionPotential Energy SurfaceSaddle PointDerivative ObservationsActive LearningOptimal TransportTrust RadiusRandom Fourier FeaturesEarth Mover's Distance
Authors
Rohit Goswami
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.