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

Surrogate-accelerated stationary point searches on potential energy surfaces are spread across two decades of papers with incompatible notation. This invited tutorial review unifies them: minimization, single-point saddle searches (the GP-dimer / minimum mode following), and double-ended path searches (GP-NEB) are one six-step Bayesian optimization loop that differs only in the inner optimization target and the acquisition criterion.

The surrogate is a Gaussian process with derivative observations on inverse-distance kernels, trained by active learning. The gain is roughly an order-of-magnitude reduction in electronic-structure evaluations, conditioned on oracle cost, search distance, and the availability of analytical forces; the review states the regime rather than claiming a universal speedup.

Production extensions are derived in full: farthest-point sampling with an intensive Earth Mover's Distance for pruning, MAP regularization for hyperparameters, an adaptive trust radius, and random Fourier features for scaling.

Pedagogical Rust code (ChemGP, https://github.com/lode-org/ChemGP) runs all three applications from the same loop and mirrors the production C++ in gpr_optim used for the published benchmarks, so every equation maps to a line of code.