Quantifying Configuration-Sampling Error in Langevin Simulations of Complex Molecular Systems
AbstractWhile 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
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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.
Fass J, Sivak DA, Crooks GE, Beauchamp KA, Leimkuhler B, Chodera JD. Quantifying Configuration-Sampling Error in Langevin Simulations of Complex Molecular Systems. Entropy. 2018; 20(5):318.Chicago/Turabian Style
Fass, Josh; Sivak, David A.; Crooks, Gavin E.; Beauchamp, Kyle A.; Leimkuhler, Benedict; Chodera, John D. 2018. "Quantifying Configuration-Sampling Error in Langevin Simulations of Complex Molecular Systems." Entropy 20, no. 5: 318.
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