Quantifying configuration-sampling error in Langevin simulations of complex molecular systems Journal Article

Authors: Fass, J.; Sivak, D. A.; Crooks, G. E.; Beauchamp, K. A.; Leimkuhler, B.; Chodera, J. D.
Article Title: Quantifying configuration-sampling error in Langevin simulations of complex molecular systems
Abstract: 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. © 2018 by the authors.
Keywords: sampling error; langevin dynamics; langevin integrators; kl divergence; molecular dynamics integrators; integrator error; baoab; velocity verlet with velocity randomization (vvvr); bussi-parrinello; shadow work; nonequilibrium free energy
Journal Title: Entropy
Volume: 20
Issue: 5
ISSN: 1099-4300
Publisher: MDPI  
Date Published: 2018-05-01
Start Page: 318
Language: English
DOI: 10.3390/e20050318
PROVIDER: scopus c7 - 318
PMCID: PMC6208357
PUBMED: 30393452
Notes: Entropy -- Cited By :2 -- Export Date: 2 January 2019 -- Article -- Source: Scopus C7
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MSK Authors
  1. John Damon Chodera
    55 Chodera
  2. Joshua Hanna Fass
    7 Fass