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首页> 外文期刊>The Journal of Chemical Physics >Variational Koopman models: Slow collective variables and molecular kinetics from short off-equilibrium simulations
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Variational Koopman models: Slow collective variables and molecular kinetics from short off-equilibrium simulations

机译：变形koopman模型：短均衡模拟中的慢集体变量和分子动力学

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摘要

Markov state models (MSMs) and master equation models are popular approaches to approximate molecular kinetics, equilibria, metastable states, and reaction coordinates in terms of a state space discretization usually obtained by clustering. Recently, a powerful generalization of MSMs has been introduced, the variational approach conformation dynamics/molecular kinetics (VAC) and its special case the time-lagged independent component analysis (TICA), which allow us to approximate slow collective variables and molecular kinetics by linear combinations of smooth basis functions or order parameters. While it is known how to estimate MSMs from trajectories whose starting points are not sampled from an equilibrium ensemble, this has not yet been the case for TICA and the VAC. Previous estimates from short trajectories have been strongly biased and thus not variationally optimal. Here, we employ the Koopman operator theory and the ideas from dynamic mode decomposition to extend the VAC and TICA to non-equilibrium data. The main insight is that the VAC and TICA provide a coefficient matrix that we call Koopman model, as it approximates the underlying dynamical (Koopman) operator in conjunction with the basis set used. This Koopman model can be used to compute a stationary vector to reweight the data to equilibrium. From such a Koopman-reweighted sample, equilibrium expectation values and variationally optimal reversible Koopman models can be constructed even with short simulations. The Koopman model can be used to propagate densities, and its eigenvalue decomposition provides estimates of relaxation time scales and slow collective variables for dimension reduction. Koopman models are generalizations of Markov state models, TICA, and the linear VAC and allow molecular kinetics to be described without a cluster discretization. Published by AIP Publishing.
机译：马尔可夫状态模型（MSM）和主型方程模型是近似分子动力学，均衡，亚稳态状态和反应坐标的流行方法，而是通过聚类通常获得的状态离散化。最近，已经介绍了MSM的强大概括，变分方法构象动态/分子动力学（VAC）及其特殊情况及其特殊情况下的时间滞后的独立分量分析（TICA），这使我们能够通过线性近似缓慢的集体变量和分子动力学顺利基础函数或订单参数的组合。虽然已知如何从轨迹中估计从均衡集合未采样的轨迹估计的MSM，但TICA和VAC尚未如此。从短轨迹的先前估计被强烈偏见，因此没有变异性。在这里，我们雇用了Koopman操作员理论和来自动态模式分解的思想，将VAC和TICA扩展到非平衡数据。主要见解是，VAC和TICA提供了我们称之为Koopman模型的系数矩阵，因为它与所使用的基础集合近似于底层动态（Koopman）操作员。该Koopman模型可用于计算静止向量以重新重量数据达平衡。从这种Koopman重新超重的样本，即使使用短模拟，也可以构建平衡期望值和变化最佳可逆的Koopman模型。 Koopman模型可用于传播密度，并且其特征值分解提供放松时间尺度和慢速减少的慢速集体变量的估计。 Koopman模型是Markov状态模型，TICA和线性VAC的概括，并允许在没有集群离散化的情况下描述分子动力学。通过AIP发布发布。

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