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

Josh Fass, David Sivak, Gavin Crooks, Kyle Beauchamp, Benedict Leimkuhler, John Chodera

Research output: Contribution to journalArticlepeer-review

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.
In \cite{Sivak:Phys.Rev.X:2013}, Sivak \textit{et al.}\ introduced a convenient approach to approximating a natural measure of error between the sampled density and the target equilibrium density, the KL divergence, in \emph{phase space}, but did not specifically address the issue of \emph{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.
Original languageEnglish
JournalEntropy
Volume20
Issue number5
DOIs
Publication statusPublished - 26 Apr 2018

Keywords

  • Langevin dynamics
  • KL divergence
  • nonequilibrium free energy
  • molecular dynamics

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