发表机构
Center for Applied Mathematics, Cornell University; R. F. Smith School of Chemical and Biomolecular Engineering, Cornell University（康奈尔大学应用数学中心; 康奈尔大学R.F.史密斯化学与生物分子工程学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
AdaptNTK是面向神经网络势的单模型框架，通过神经正切核特征空间的正则化马氏距离量化不确定性，在rMD17和Transition-1X主动学习任务中实现低力误差与2.6倍加速，提升了数据效率。
AI 中文摘要
机器学习原子间势架起了量子化学精度与经典计算速度之间的桥梁，使能达到第一性原理精度的分子动力学模拟。其可靠性常通过主动学习提升，主动学习通过识别分布外的不确定构型迭代扩充训练集。现有不确定性量化方法常存在计算成本与可靠性间的权衡，且在组装获取批次时通常无法考虑冗余。本文提出AdaptNTK，一种单模型框架，将不确定性量化为经验神经正切核（NTK）特征空间中的正则化马氏距离。由于获取阶段NTK特征固定，不确定性取决于获取的构型而非其参考标签，这允许在每次选择后递归更新不确定性而无需重新训练，减少获取批次内的冗余。在留出的rMD17数据上，AdaptNTK与力误差的平均相关性最高（斯皮尔曼0.68，皮尔逊0.71），且误差保持能力与三成员集成模型相当。在主动学习实验中，AdaptNTK在rMD17和Transition-1X上均实现最低力误差，尤其在Transition-1X的过渡态构型上表现突出。与集成模型相比，AdaptNTK在每个Transition-1X循环中实现2.6倍加速，为数据高效的主动学习提供了高效的单模型不确定性估计与顺序更新。
英文摘要
Machine learning interatomic potentials bridge the gap between quantum chemical precision and classical computational speed, enabling molecular dynamics simulations with first-principles accuracy. Their reliability is often improved through active learning, which iteratively expands the training set by identifying uncertain, out-of-distribution configurations. Existing uncertainty-quantification methods often involve a trade-off between computational cost and reliability, and generally cannot account for redundancy as an acquisition batch is assembled. Here, we introduce AdaptNTK, a single-model framework that measures uncertainty as a regularized Mahalanobis distance in empirical neural tangent kernel (NTK) feature space. With the NTK features fixed during acquisition, the uncertainty depends on the acquired configurations but not their reference labels. This allows the uncertainty to be updated recursively after each selection without retraining, reducing redundancy within an acquisition batch. On held-out rMD17 data, AdaptNTK achieves the highest mean correlations with force errors (Spearman 0.68, Pearson 0.71) and matches a three-member ensemble in error retention. In active learning experiments, AdaptNTK achieves the lowest force errors across rMD17 and Transition-1X, with particularly strong performance on transition-state configurations in Transition-1X. AdaptNTK provides a 2.6-fold speedup per Transition-1X cycle relative to the ensemble, providing efficient single-model uncertainty estimation with sequential updates for data-efficient active learning.
