Quantifying Configuration-Sampling Error in Langevin Simulations of Complex Molecular Systems
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 du...
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MDPI AG
2018-04-01
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Online Access: | http://www.mdpi.com/1099-4300/20/5/318 |
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author | Josh Fass David A. Sivak Gavin E. Crooks Kyle A. Beauchamp Benedict Leimkuhler John D. Chodera |
author_facet | Josh Fass David A. Sivak Gavin E. Crooks Kyle A. Beauchamp Benedict Leimkuhler John D. Chodera |
author_sort | Josh Fass |
collection | DOAJ |
description | 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. |
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issn | 1099-4300 |
language | English |
last_indexed | 2024-04-11T13:46:31Z |
publishDate | 2018-04-01 |
publisher | MDPI AG |
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spelling | doaj.art-b60a535852db43bc8f751bb43eb0c2802022-12-22T04:21:01ZengMDPI AGEntropy1099-43002018-04-0120531810.3390/e20050318e20050318Quantifying Configuration-Sampling Error in Langevin Simulations of Complex Molecular SystemsJosh Fass0David A. Sivak1Gavin E. Crooks2Kyle A. Beauchamp3Benedict Leimkuhler4John D. Chodera5Tri-Institutional PhD Program in Computational Biology & Medicine, New York, NY 10065, USADepartment of Physics, Simon Fraser University, Burnaby, BC V5A 1S6, CanadaRigetti Computing, Berkeley, CA 94710, USACounsyl, South San Francisco, CA 94080, USASchool of Mathematics and Maxwell Institute of Mathematical Sciences, James Clerk Maxwell Building, Kings Buildings, University of Edinburgh, Edinburgh EH9 3FD, UKComputational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, NY 10065, USAWhile 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.http://www.mdpi.com/1099-4300/20/5/318Langevin dynamicsLangevin integratorsKL divergencenonequilibrium free energymolecular dynamics integratorsintegrator errorsampling errorBAOABvelocity verlet with velocity randomization (VVVR)Bussi-Parrinelloshadow workintegrator error |
spellingShingle | Josh Fass David A. Sivak Gavin E. Crooks Kyle A. Beauchamp Benedict Leimkuhler John D. Chodera Quantifying Configuration-Sampling Error in Langevin Simulations of Complex Molecular Systems Entropy 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 |
title | Quantifying Configuration-Sampling Error in Langevin Simulations of Complex Molecular Systems |
title_full | Quantifying Configuration-Sampling Error in Langevin Simulations of Complex Molecular Systems |
title_fullStr | Quantifying Configuration-Sampling Error in Langevin Simulations of Complex Molecular Systems |
title_full_unstemmed | Quantifying Configuration-Sampling Error in Langevin Simulations of Complex Molecular Systems |
title_short | Quantifying Configuration-Sampling Error in Langevin Simulations of Complex Molecular Systems |
title_sort | quantifying configuration sampling error in langevin simulations of complex molecular systems |
topic | 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 |
url | http://www.mdpi.com/1099-4300/20/5/318 |
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