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Entropy 2018, 20(5), 318; https://doi.org/10.3390/e20050318

Quantifying Configuration-Sampling Error in Langevin Simulations of Complex Molecular Systems

1
Tri-Institutional PhD Program in Computational Biology & Medicine, New York, NY 10065, USA
2
Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, NY 10065, USA
3
Department of Physics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada
4
Rigetti Computing, Berkeley, CA 94710, USA
5
Counsyl, South San Francisco, CA 94080, USA
6
School of Mathematics and Maxwell Institute of Mathematical Sciences, James Clerk Maxwell Building, Kings Buildings, University of Edinburgh, Edinburgh EH9 3FD, UK
*
Author to whom correspondence should be addressed.
Received: 12 February 2018 / Revised: 14 April 2018 / Accepted: 15 April 2018 / Published: 26 April 2018
(This article belongs to the Special Issue Understanding Molecular Dynamics via Stochastic Processes)
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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. View Full-Text
Keywords: Langevin dynamics; Langevin integrators; KL divergence; nonequilibrium free energy; molecular dynamics integrators; integrator error; sampling error; BAOAB; velocity verlet with velocity randomization (VVVR); Bussi-Parrinello; shadow work; integrator error Langevin dynamics; Langevin integrators; KL divergence; nonequilibrium free energy; molecular dynamics integrators; integrator error; sampling error; BAOAB; velocity verlet with velocity randomization (VVVR); Bussi-Parrinello; shadow work; integrator error
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Fass, J.; Sivak, D.A.; Crooks, G.E.; Beauchamp, K.A.; Leimkuhler, B.; Chodera, J.D. Quantifying Configuration-Sampling Error in Langevin Simulations of Complex Molecular Systems. Entropy 2018, 20, 318.

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