PT - JOURNAL ARTICLE
AU - Fass, Josh
AU - Sivak, David A.
AU - Crooks, Gavin E.
AU - Beauchamp, Kyle A.
AU - Leimkuhler, Ben
AU - Chodera, John D.
TI - Quantifying configuration-sampling error in Langevin simulations of complex molecular systems
AID - 10.1101/266619
DP - 2018 Jan 01
TA - bioRxiv
PG - 266619
4099 - http://biorxiv.org/content/early/2018/02/16/266619.short
4100 - http://biorxiv.org/content/early/2018/02/16/266619.full
AB - While Langevin integrators are widely popular in the study of equilibrium properties of complex systems, it is challenging to estimate the 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 quantifying the a natural measure of distribution 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 error 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.