自適應修剪以增強高斯過程加速鞍點搜索的魯棒性並降低計算開銷

Adaptive Pruning for Increased Robustness and Reduced Computational Overhead in Gaussian Process Accelerated Saddle Point Searches

October 7, 2025

作者: Rohit Goswami, Hannes Jónsson

cs.AI

摘要

高斯過程（GP）迴歸提供了一種策略，通過減少需要評估能量及其對原子座標導數的次數，來加速高維能量面上的鞍點搜索。然而，超參數優化中的計算開銷可能很大，使得該方法效率低下。如果搜索過於深入GP模型未能充分表示的區域，也可能導致失敗。本文通過使用幾何感知的最優傳輸度量以及一種主動修剪策略來解決這些挑戰，該策略在遠點採樣中對每種原子類型的Wasserstein-1距離求和，選擇固定大小的幾何多樣性配置子集，以避免隨著觀測次數增加而迅速增長的GP更新成本。通過引入置換不變度量來增強穩定性，該度量為早期停止提供了可靠的信任半徑，並對信號方差的增長施加對數障礙懲罰。這些基於物理動機的算法改進，在來自先前發表的化學反應數據集的238個挑戰性配置上，將平均計算時間減少到不到一半，證明了其有效性。通過這些改進，GP方法被確立為一種穩健且可擴展的算法，用於在能量和原子力評估需要大量計算工作時加速鞍點搜索。

English

Gaussian process (GP) regression provides a strategy for accelerating saddle point searches on high-dimensional energy surfaces by reducing the number of times the energy and its derivatives with respect to atomic coordinates need to be evaluated. The computational overhead in the hyperparameter optimization can, however, be large and make the approach inefficient. Failures can also occur if the search ventures too far into regions that are not represented well enough by the GP model. Here, these challenges are resolved by using geometry-aware optimal transport measures and an active pruning strategy using a summation over Wasserstein-1 distances for each atom-type in farthest-point sampling, selecting a fixed-size subset of geometrically diverse configurations to avoid rapidly increasing cost of GP updates as more observations are made. Stability is enhanced by permutation-invariant metric that provides a reliable trust radius for early-stopping and a logarithmic barrier penalty for the growth of the signal variance. These physically motivated algorithmic changes prove their efficacy by reducing to less than a half the mean computational time on a set of 238 challenging configurations from a previously published data set of chemical reactions. With these improvements, the GP approach is established as, a robust and scalable algorithm for accelerating saddle point searches when the evaluation of the energy and atomic forces requires significant computational effort.