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

View ORCID ProfileJosh Fass, View ORCID ProfileDavid A. Sivak, Gavin E. Crooks, View ORCID ProfileKyle A. Beauchamp, View ORCID ProfileBen Leimkuhler, John D. Chodera
doi: https://doi.org/10.1101/266619
Josh Fass
1Tri-Institutional PhD Program in Computational Biology & Medicine, New York, NY 10065;
6Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, NY 10065; ,
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  • For correspondence: josh.fass@choderalab.org john.chodera@choderalab.org
David A. Sivak
2Department of Physics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada; ,
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  • For correspondence: dsivak@sfu.ca
Gavin E. Crooks
3Rigetti Computing;
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  • For correspondence: gec@threeplusone.com
Kyle A. Beauchamp
4Counsyl, South San Francisco, CA 94080;
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  • For correspondence: kyleabeauchamp@gmail.com
Ben Leimkuhler
5School of Mathematics and Maxwell Institute of Mathematical Sciences, James Clerk Maxwell Building, Kings Buildings, University of Edinburgh, Edinburgh, EH9 3JZ, UK; ,
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  • For correspondence: B.Leimkuhler@ed.ac.uk
John D. Chodera
6Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, NY 10065; ,
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  • For correspondence: john.chodera@choderalab.org john.chodera@choderalab.org
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Abstract

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.

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The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY 4.0 International license.
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Posted February 16, 2018.
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Quantifying configuration-sampling error in Langevin simulations of complex molecular systems
Josh Fass, David A. Sivak, Gavin E. Crooks, Kyle A. Beauchamp, Ben Leimkuhler, John D. Chodera
bioRxiv 266619; doi: https://doi.org/10.1101/266619
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Quantifying configuration-sampling error in Langevin simulations of complex molecular systems
Josh Fass, David A. Sivak, Gavin E. Crooks, Kyle A. Beauchamp, Ben Leimkuhler, John D. Chodera
bioRxiv 266619; doi: https://doi.org/10.1101/266619

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