Rejection-free Monte Carlo for liquid water

Date

Apr 27, 2018

Time

11:00 AM - 12:00 PM

Speaker

Michael Faulkner

Affiliation

University of Bristol

Language

en

Main Topic

Biologie

Other Topics

Biologie

Host

Vojtech Kaiser, Sbalzarini-Group

Description

Markov-chain Monte Carlo methods are used throughout the statistical sciences. The majority of algorithms are (time) reversible and therefore satisfy the detailed-balance condition, which ensure convergence to the correct probability distribution. However, reversible Markov processes often lead to slow, diffusive behaviour on the configuration space. The event-chain Monte Carlo (ECMC) algorithm [1] circumvents this by augmenting the configuration space with a lifting variable [2] to connect two nonreversible Markov sub-processes that strictly evolve in opposite directions on the original configuration space. This is the case for two-particle interactions in one spatial dimension, but generalizes to multiple particles and interactions in higher dimensions. Nonreversibility effectively drives the system through the original configuration space, rather than leaving it to meander through diffusively, resulting in shorter ECMC mixing times than those of reversible Markov processes [3]. This lifted Markov process is formally rejection free and satisfies skewed detailed balance on the augmented space, the latter of which ensures convergence to the correct distribution. In this talk, I will introduce nonreversible Markov processes and skewed detailed balance, before outlining rejection-free ECMC. I will then discuss the application to all-atom models of liquid water [4]. This uses the locally charge-neutral property of water molecules to reduce the Coulomb scaling to O(N ln(N)) (N the number of water molecules) with neither an interpolating mesh, nor a thermostat, nor spatial cut-offs on the lengthscale of the interaction potentials. [1] Bernard et al, Phys. Rev. E 80, 056704 (2009) [2] P. Diaconis et al, Ann. Appl. Probab. 10, 726 (2000) [3] Kapfer and Krauth, Phys. Rev. Lett. 119, 240603 (2017); Lei and Krauth, arXiv:1711.08375 (2017) [4] Faulkner, Qin, Maggs, Krauth, arXiv:1804.05795 (2018)

Last modified: Apr 28, 2018, 9:40:00 AM