Quantifying Configuration-Sampling Error in Langevin Simulations of Complex Molecular Systems
Quantifying Configuration-Sampling Error in Langevin Simulations of Complex Molecular Systems
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DOI：
10.3390/e20050318
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发表时间：
2018-05-01
期刊：
影响因子：
2.7
通讯作者：
Chodera, John D.
中科院分区：
文献类型：
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作者：
Fass, Josh;Sivak, David A.;Chodera, John D.
虽然朗之万积分器在复杂系统的平衡性质的研究中很受欢迎，但估计时间步长引起的离散化误差是具有挑战性的：由于使用有限的积分时间步长，采样的相空间或配置空间概率密度偏离所需目标密度的程度。Sivak等人，引入了一种方便的方法来近似采样密度和目标平衡密度之间的误差的自然测量，Kullback-Leibler（KL）发散，在相空间中，但没有具体解决构型空间性质的问题，这在分子模拟中更常见。在这里，我们介绍了一个变种，这种近平衡估计能够测量的配置空间的边缘密度的错误，验证它对一个复杂的，但精确的嵌套蒙特卡罗估计，以显示它再现的KL发散高保真。为了说明它的效用，我们采用这种新的近平衡估计评估索赔，最近提出的朗之万积分引入极小的配置空间密度误差的稳定性限制，没有额外的计算费用。最后，我们展示了如何量化采样偏差的这种方法可以应用到各种各样的随机积分器以下一个简单的程序来计算适当的影子工作，并描述它如何可以扩展到量化的误差在任意边际或条件分布的利益。
While Langevin integrators are popular in the study of equilibrium properties of complex systems, it is challenging to estimate the timestep-induced discretization error: the degree to which the sampled phase-space or configuration-space probability density departs from the desired target density due to the use of a finite integration timestep. Sivak et al., introduced a convenient approach to approximating a natural measure of error between the sampled density and the target equilibrium density, the Kullback-Leibler (KL) divergence, in phase space, but did not specifically address the issue of configuration-space properties, which are much more commonly of interest in molecular simulations. Here, we introduce a variant of this near-equilibrium estimator capable of measuring the error in the configuration-space marginal density, validating it against a complex but exact nested Monte Carlo estimator to show that it reproduces the KL divergence with high fidelity. To illustrate its utility, we employ this new near-equilibrium estimator to assess a claim that a recently proposed Langevin integrator introduces extremely small configuration-space density errors up to the stability limit at no extra computational expense. Finally, we show how this approach to quantifying sampling bias can be applied to a wide variety of stochastic integrators by following a straightforward procedure to compute the appropriate shadow work, and describe how it can be extended to quantify the error in arbitrary marginal or conditional distributions of interest.