%0 Journal Article
%A Fass, Josh
%A Sivak, David A.
%A Crooks, Gavin E.
%A Beauchamp, Kyle A.
%A Leimkuhler, Benedict
%A Chodera, John D.
%T Quantifying configuration-sampling error in Langevin simulations of complex molecular systems
%D 2018
%R 10.1101/266619
%J bioRxiv
%P 266619
%X 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. In [1], Sivak et al. introduced a convenient approach to approximating a natural measure of error between the sampled density and the target equilibrium density, the 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.
%U https://www.biorxiv.org/content/biorxiv/early/2018/04/15/266619.full.pdf