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

Entropy

DavidA. Sivak¹  Benedict Leimkuhler²  GavinE. Crooks³  KyleA. Beauchamp⁴  JohnD. Chodera⁵  Josh Fass⁶ 

[1] Medicine, New York, NY 10065, USA;Counsyl, South San Francisco, CA 94080, USA;Department of Physics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada;Rigetti Computing, Berkeley, CA 94710, USA;School of Mathematics and Maxwell Institute of Mathematical Sciences, James Clerk Maxwell Building, Kings Buildings, University of Edinburgh, Edinburgh EH9 3FD, UK;;Tri-Institutional PhD Program in Computational Biology &

关键词: 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;   

DOI  :  10.3390/e20050318

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown