基于张量的分子动力学近似：生成元学习、反应坐标与增量更新
Tensor-based Approximation of Molecular Kinetics: Generator Learning, Reaction Coordinates and Incremental Updating
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中文总结 AI 辅助
提出基于张量生成元近似的分子动力学长时标分析方法，利用张量列格式高效求解特征值问题，支持反应坐标增量更新，并在快速折叠蛋白模拟中验证了识别亚稳态和转变的有效性。
中文摘要 AI 辅助
我们提出了一种基于张量的无穷小生成元近似方法，用于分析分子动力学模拟的长时标动力学——亚稳态和转变时标。我们从低能生成元特征值的变分近似出发，使用张量积基对相应的特征值问题进行离散化。我们推导了张量列（TT）格式下所得张量算子的解析表达式，并提供了求解相应线性问题的高效算法。我们还处理了状态相关扩散场的情况，这在反应坐标下工作时是相关的。我们展示了如何在不从头求解变分问题的情况下逐步增加反应坐标的数量。利用快速折叠蛋白的MD模拟和TICA坐标作为反应坐标，我们证明了所提方法在识别长时标转变和亚稳态方面的有效性。
英文摘要
We present an approach to analyze long-timescale kinetics of molecular dynamics simulations - meta-stable states and transition timescales - by a tensor-based approximation of the infinitesimal generator. We start from the variational approximation of low-lying generator eigenvalues, and discretize the associated eigenvalue problem using a tensor-product basis. We derive analytical expressions for the resulting tensor operators in tensor train (TT) format, and provide efficient algorithms to solve the corresponding linear problems. We also treat the case of a state-dependent diffusion field, which is relevant when working in reaction coordinates. We show how the number of reaction coordinates can be gradually increased without having to solve the variational problem from scratch. Using MD simulations of fast-folding proteins and TICA coordinates as reaction coordinates, we demonstrate the effectiveness of the proposed method at identifying long-timescale transitions and meta-stable states.
