Bayesian Optimization with Gaussian Processes to Accelerate Stationary Point Searches
This work addresses computational bottlenecks in chemistry and materials science by providing an efficient method for stationary point searches, though it appears incremental as an extension of existing Bayesian Optimization techniques.
The paper tackles the problem of accelerating stationary point searches on potential energy surfaces by presenting a unified Bayesian Optimization framework with Gaussian processes, which reduces required evaluations by an order of magnitude while maintaining accuracy.
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.