Building local surrogates to accelerate stationary point searches on potential energy surfaces spans decades of effort. Done correctly, surrogates can reduce the number of expensive electronic structure evaluations by roughly an order of magnitude while preserving the accuracy of the underlying theory, with the gain depending on oracle cost, search distance, and the availability of analytical forces. We present a unified Bayesian optimization view of minimization, single-point saddle searches, and double-ended path searches: all three share one six-step surrogate loop and differ only in the inner optimization target and the acquisition criterion. The framework uses Gaussian process regression with derivative observations, inverse-distance kernels, and active learning, and we develop optional extensions for production use, including farthest-point sampling with the Earth Mover's Distance, MAP regularization, an adaptive trust radius, and random Fourier features for scaling. Accompanying pedagogical Rust code demonstrates that all three applications use the same Bayesian optimization loop, bridging the gap between theoretical formulation and practical execution.

翻译：构建局部代理模型以加速势能面上驻点搜索的研究已历经数十载。合理运用代理模型可在保持底层理论精度的前提下，将昂贵电子结构评估次数减少约一个数量级，其增益取决于Oracle成本、搜索距离及解析力的可用性。本文提出统一的贝叶斯优化视角，涵盖极小化、单点鞍点搜索与双端路径搜索三类问题：三者共享六步代理循环，仅在内层优化目标与采集准则上存在差异。该框架采用含导数观测的高斯过程回归、逆距离核函数与主动学习，并开发了面向生产环境的可选扩展，包括基于推土机距离的最远点采样、最大后验正则化、自适应信赖域半径及用于规模扩展的随机傅里叶特征。配套教学用Rust代码表明，三类应用均遵循相同的贝叶斯优化循环，从而弥合了理论公式与工程实现之间的鸿沟。