用高斯过程贝叶斯优化加速势能面驻点搜索，减少计算量近十倍。
A Tutorial Review of Bayesian Optimization with Gaussian Processes to Accelerate Stationary Point Searches
- 统一框架：三种搜索共用六步代理循环，仅目标函数与采集准则不同。
- 实测可减少约九成电子结构计算，依赖于初始成本与力信息可用性。
- 适合计算化学与材料模拟研究者，代码开源便于落地应用。
构建局部代理模型以加速势能面上驻点搜索已持续数十年。若正确实施，代理模型可使昂贵的电子结构计算次数减少约一个数量级，同时保持理论精度，其增益取决于查询代价、搜索距离及解析力的可得性。本文提出统一的贝叶斯优化视角，涵盖最小化、单点鞍点搜索与双端路径搜索：三者共享同一六步代理循环，仅内层优化目标与采集准则不同。该框架采用含导数观测的高斯过程回归、反距离核函数与主动学习，并开发了适用于生产环境的扩展功能，包括基于地球移动距离的最远点采样、最大后验正则化、自适应信任半径以及用于可扩展性的随机傅里叶特征。配套教学性质的Rust代码证明三类应用使用相同贝叶斯优化流程，弥合了理论与实践之间的鸿沟。
原文摘要 · Abstract (English)
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.
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