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.

翻译：通过构建局部代理模型加速势能面上驻点的探索已历经数十年的研究。正确实施的代理模型能在保持底层理论精度的同时，将所需计算量降低一个数量级。本文提出一种统一的贝叶斯优化框架，通过统一的六步代理循环处理极小值点搜索、单端鞍点搜索及双端鞍点搜索，其差异仅体现在内部优化目标与采集准则的设计上。该框架采用包含导数观测的高斯过程回归、反距离核函数及主动学习策略。通过融合最远点采样的最优传输高斯过程扩展（基于推土机距离）、基于方差屏障与振荡检测的MAP正则化以及自适应信任半径机制，我们在保持基础方法论一致性的同时提升了算法的精度与效率。此外，我们展示了随机傅里叶特征技术能够解耦超参数训练与预测过程，从而为高维系统提供优越的扩展性能。配套的Rust教学代码表明所有应用均使用完全相同的贝叶斯优化循环，有效弥合了理论框架与工程实践之间的鸿沟。