Hard-disk dipoles and non-reversible Markov chains

Hoellmer, Philipp; Maggs, A. C.; Krauth, Werner

doi:10.1063/5.0080101

Cited by 6 publications

(6 citation statements)

References 41 publications

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“…A number of inequivalent options have been constructed for the update of active particles within event-chain Monte Carlo 23 , 39 . Similar flexibility is possible in the updating of velocities 29 , 30 , 40 , 41 , as well as in parallelizing the algorithm 24 , 42 . The original straight variant is most efficient for simple hard disks 29 , 33 , but is completely inappropriate for hard-disk dipoles 41 and water molecules 43 that require the exploration of internal rotational degrees of freedom.…”

Section: Resultsmentioning

confidence: 99%

“…Similar flexibility is possible in the updating of velocities 29 , 30 , 40 , 41 , as well as in parallelizing the algorithm 24 , 42 . The original straight variant is most efficient for simple hard disks 29 , 33 , but is completely inappropriate for hard-disk dipoles 41 and water molecules 43 that require the exploration of internal rotational degrees of freedom. In this paper, we generalize Newtonian event-chain Monte Carlo 30 from systems akin to the hard-disk system to molecular systems (see Methods section).…”

Section: Resultsmentioning

confidence: 99%

“…Newtonian event-chain Monte Carlo was originally only formulated for the hard-sphere model that contains peculiar stepwise-changing two-body factor potentials 30 . Among various event-chain Monte Carlo variants, it was shown to escape faster from sparse hard-disk packings 57 and to produce favorable rotation dynamics in tethered hard-disk dipoles 41 . Its superiority is confirmed for the rotation dynamics of SPC/Fw water molecules in this paper, but requires its generalization to smooth factor potentials that depend on an arbitrary number of atom positions.…”

Section: Methodsmentioning

confidence: 99%

“…Samples of all-atom configurations that can be used to compute observables are taken at periodic time intervals 30 . Furthermore, Newtonian event-chain Monte Carlo requires resampling of the all-atom velocity and the active atom i at periodic time intervals in order to be irreducible 41 . We sample and i from their respective stationary distributions and .…”

Section: Methodsmentioning

confidence: 99%

See 3 more Smart Citations

Fast, approximation-free molecular simulation of the SPC/Fw water model using non-reversible Markov chains

Höllmer,

Maggs,

Krauth

2024

Sci Rep

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In a world made of atoms, computer simulations of molecular systems such as proteins in water play an enormous role in science. Software packages for molecular simulation have been developed for decades. They all discretize Hamilton’s equations of motion and treat long-range potentials through cutoffs or discretization of reciprocal space. This introduces severe approximations and artifacts that must be controlled algorithmically. Here, we bring to fruition a paradigm for molecular simulation that relies on modern concepts in statistics to explore the thermodynamic equilibrium with an exact and efficient non-reversible Markov process. It is free of all discretizations, approximations, and cutoffs. We explicitly demonstrate that this approach reaches a break-even point with traditional molecular simulation performed at high precision, but without any of its approximations. We stress the potential of our paradigm for crucial applications in biophysics and other fields, and as a practical approach to molecular simulation. We set out a strategy to reach our goal of rigorous molecular simulation.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

See 2 more Smart Citations

Fast, approximation-free molecular simulation of the SPC/Fw water model using non-reversible Markov chains

Höllmer,

Maggs,

Krauth

2024

Sci Rep

View full text Add to dashboard Cite

show abstract

“…In fact, the research on improved MC algorithms is still vivid. Beyond PT [8] and the isoenergetic updates [9,10], relevant research strategies focus on non-reversible schemes [74][75][76][77], chiefly event-driven algorithms [78,79], on tuning the acceptance rates [80], or on exploiting population annealing [81,82]. Notice also that neural samplers could be further improved via hierarchical autoregressive networks [83].…”

Section: Discussionmentioning

confidence: 99%

Accelerating equilibrium spin-glass simulations using quantum annealers via generative deep learning

et al. 2023

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Adiabatic quantum computers, such as the quantum annealers commercialized by D-Wave Systems Inc., are routinely used to tackle combinatorial optimization problems. In this article, we show how to exploit them to accelerate equilibrium Markov chain Monte Carlo simulations of computationally challenging spin-glass models at low but finite temperatures. This is achieved by training generative neural networks on data produced by a D-Wave quantum annealer, and then using them to generate smart proposals for the Metropolis-Hastings algorithm. In particular, we explore hybrid schemes by combining single spin-flip and neural proposals, as well as D-Wave and classical Monte Carlo training data. The hybrid algorithm outperforms the single spin-flip Metropolis-Hastings algorithm. It is competitive with parallel tempering in terms of correlation times, with the significant benefit of a much shorter equilibration time.

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Sparse Hard-Disk Packings and Local Markov Chains

Hoellmer

Nicolas

et al. 2022

J Stat Phys

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We propose locally stable sparse hard-disk packings, as introduced by Böröczky, as a model for the analysis and benchmarking of Markov-chain Monte Carlo (MCMC) algorithms. We first generate such Böröczky packings in a square box with periodic boundary conditions and analyze their properties. We then study how local MCMC algorithms, namely the Metropolis algorithm and several versions of event-chain Monte Carlo (ECMC), escape from configurations that are obtained from the packings by slightly reducing all disk radii by a relaxation parameter. We obtain two classes of ECMC, one in which the escape time varies algebraically with the relaxation parameter (as for the local Metropolis algorithm) and another in which the escape time scales as the logarithm of the relaxation parameter. A scaling analysis is confirmed by simulation results. We discuss the connectivity of the hard-disk sample space, the ergodicity of local MCMC algorithms, as well as the meaning of packings in the context of the NPT ensemble. Our work is accompanied by open-source, arbitrary-precision software for Böröczky packings (in Python) and for straight, reflective, forward, and Newtonian ECMC (in Go).

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Hard-disk dipoles and non-reversible Markov chains

Cited by 6 publications

References 41 publications

Fast, approximation-free molecular simulation of the SPC/Fw water model using non-reversible Markov chains

Fast, approximation-free molecular simulation of the SPC/Fw water model using non-reversible Markov chains

Accelerating equilibrium spin-glass simulations using quantum annealers via generative deep learning

Sparse Hard-Disk Packings and Local Markov Chains

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