论文标题
Langevin动力学的路径概率比 - 精确而近似
Path probability ratios for Langevin dynamics -- exact and approximate
论文作者
论文摘要
路径重新加权是从偏置模拟中估算动态性能的一种主要精确方法 - 前提是路径概率比与模拟中使用的随机积分器匹配。先前报道的路径概率比与过度阻尼Langevin动力学的Euler-Maruyama方案相匹配。由于MD模拟使用Langevin动力学，而不是过度抑制Langevin动力学，因此这严重阻碍了路径重新加权方法的应用。在这里，我们得出了由Langevin Leapfrog Integrator的变体传播的Langevin Dynamics的路径概率$ M_L $。这种新的路径概率比允许该集成器传播的langevin动力学的精确重新加权。我们还表明，先前派生的近似路径概率比$ m _ {\ mathrm {左右}} $与确切的$ m_l $仅与$ \ mathcal {o}（ξ^4Δt^4）$不同，从而产生了非常准确的动态重新加权结果。 （$ΔT$是集成时间步骤，$ξ$是碰撞率。）测试结果并以丁烷为例探索了路径牵引的效率。
Path reweighting is a principally exact method to estimate dynamic properties from biased simulations - provided that the path probability ratio matches the stochastic integrator used in the simulation. Previously reported path probability ratios match the Euler-Maruyama scheme for overdamped Langevin dynamics. Since MD simulations use Langevin dynamics rather than overdamped Langevin dynamics, this severely impedes the application of path reweighting methods. Here, we derive the path probability ratio $M_L$ for Langevin dynamics propagated by a variant of the Langevin Leapfrog integrator. This new path probability ratio allows for exact reweighting of Langevin dynamics propagated by this integrator. We also show that a previously derived approximate path probability ratio $M_{\mathrm{approx}}$ differs from the exact $M_L$ only by $\mathcal{O}(ξ^4Δt^4)$, and thus yields highly accurate dynamic reweighting results. ($Δt$ is the integration time step, $ξ$ is the collision rate.) The results are tested and the efficiency of path-reweighting is explored using butane as an example.
