截断自动稀疏微分用于机器学习原子间势
Truncated automatic sparse differentiation for machine learning interatomic potentials
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中文总结 AI 辅助
针对机器学习原子间势中高阶导数计算昂贵的问题，提出利用相互作用稀疏性进行自动稀疏微分，并通过截断远距离微小Hessian元素实现数量级加速，且对预测影响极小。
中文摘要 AI 辅助
机器学习原子间势（MLIPs）学习从原子位置到势能的映射。力，即该能量的负梯度，驱动分子动力学，并可通过自动微分轻松获得。高阶导数，尤其是Hessian矩阵，描述了集体运动并允许直接预测实验可观测量，但对于大系统而言，这些导数被认为在计算上难以实现。我们提出一个解决方案：在物理系统中，相互作用随距离衰减，大多数MLIPs通过有限感受野内的消息传递来利用这种局域性。这意味着高阶导数的稀疏性及其随距离的衰减。这种结构可以利用自动稀疏微分（ASD）来加以利用。我们解释了如何计算MLIP导数的稀疏模式，并证明对于多个基础MLIPs，ASD能够精确计算大型多孔材料的完整Hessian矩阵，但速度提升最多仅为适度。更大的收益来自截断ASD：丢弃远距离原子之间微小但非零的Hessian矩阵元素，可实现数量级的加速，而对预测可观测量影响可忽略不计。
英文摘要
Machine learning interatomic potentials (MLIPs) learn the mapping from atomic positions to potential energy. The forces, the negative gradient of this energy, drive molecular dynamics and are readily obtained using automatic differentiation. Higher-order derivatives, most notably the Hessian, describe collective motion and allow the direct prediction of experimental observables, but are considered computationally inaccessible for large systems. We suggest a solution: in physical systems, interactions decay with distance, and most MLIPs build on this locality through message passing up to a finite receptive field. This implies both sparsity of higher-order derivatives and their decay with distance. This structure can be exploited using automatic sparse differentiation (ASD). We explain how to compute the sparsity pattern for MLIP derivatives and demonstrate that, for multiple foundation MLIPs, ASD computes full Hessians of large porous materials exactly, but with modest speedups at best. The larger gains come from truncated ASD: discarding small, but nonzero, Hessian entries between distant atoms yields order-of-magnitude speedups with negligible impact on predicted observables.
发表机构
- EPFL（洛桑联邦理工学院）
- Technical University of Berlin（柏林工业大学）
- BIFOLD – Berlin Institute for the Foundations of Learning and Data（BIFOLD——柏林学习与数据基础研究所）
机构由 AI 辅助整理，请以论文原文为准。
