Piecewise deterministic Markov processes for scalable Monte Carlo on restricted domains

Bierkens, Joris; Bouchard‐Côté, Alexandre; Doucet, Arnaud; Duncan, Anthony; Fearnhead, Paul; Lienart, Thibaut; Roberts, Gareth O.; Vollmer, Sebastian J.

doi:10.1016/j.spl.2018.02.021

Cited by 51 publications

(66 citation statements)

References 25 publications

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“…(7) is much smaller than that in eq. (8). We expect that the case b = L/N leads to larger amplitude movements of the active particle i, at the same time the transfer of activity is equally often toward i + 1 and toward i − 1, and characterizes the detailed ECMC dynamics.…”

Section: Ecmc For Harmonic Interactionsmentioning

confidence: 95%

Event-chain Monte Carlo with factor fields

2019

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We study the dynamics of one-dimensional (1D) interacting particles simulated with the eventchain Monte Carlo algorithm (ECMC). We argue that previous versions of the algorithm suffer from a mismatch in the factor potential between different particle pairs (factors) and show that in 1D models, this mismatch is overcome by factor fields. ECMC with factor fields is motivated, in 1D, for the harmonic model, and validated for the Lennard-Jones model as well as for hard spheres. In 1D particle systems with short-range interactions, autocorrelation times generally scale with the second power of the system size for reversible Monte Carlo dynamics, and with its first power for regular ECMC and for molecular-dynamics. We show, using numerical simulations, that they grow only with the square root of the systems size for ECMC with factor fields. Mixing times, which bound the time to reach equilibrium from an arbitrary initial configuration, grow with the first power of the system size.arXiv:1812.02494v1 [cond-mat.stat-mech]

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Section: Ecmc For Harmonic Interactionsmentioning

confidence: 95%

Event-chain Monte Carlo with factor fields

2019

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“…In contrast, the parameters of the physical system are accessed only using the modules of the specific setting (for example the setting.hypercubic setting module). 6 The setting package and its modules are initialized by classes which inherit from the abstract Setting class. The HypercuboidSetting class defines only the hypercuboid setting, the HypercubicSetting class, however, sets up both the hypercubic setting and the hypercuboid setting modules together with the setting package.…”

Section: Globally Used Modulesmentioning

confidence: 99%

“…ECMC has been successfully applied to the classic Nbody all-atom problem in statistical physics [4,17]. The algorithm implements the time evolution of a piecewise non-interacting, deterministic, system [6]. Each straight-line, non-interacting leg of this time evolution terminates in an event, defined through the event time at which it takes place and through the out-state, the updated starting configuration for the ensuing leg.…”

Section: Introductionmentioning

confidence: 99%

JeLLyFysh-Version1.0 — a Python application for all-atom event-chain Monte Carlo

Hoellmer

Qin

Faulkner

et al. 2020

Computer Physics Communications

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We present JeLLyFysh-Version1.0, an open-source Python application for eventchain Monte Carlo (ECMC), an event-driven irreversible Markov-chain Monte Carlo algorithm for classical N -body simulations in statistical mechanics, biophysics and electrochemistry. The application's architecture closely mirrors the mathematical formulation of ECMC. Local potentials, long-ranged Coulomb interactions and multi-body bending potentials are covered, as well as bounding potentials and cell systems including the cell-veto algorithm. Configuration files illustrate a number of specific implementations for interacting atoms, dipoles, and water molecules.

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“…For 3 The simulator we use also allows for fast calculation of the gradients of the log likelihood by the adjoint procedure [16], so that HMC-type samplers can be run. 4 The optimization algorithm used here is BFGS [11], but in principle any other could be used.…”

Section: Target Measuresmentioning

confidence: 99%

“…Admittedly, this observation only applies when the size of the domain is known a priori. See also[4].…”

mentioning

confidence: 99%

Reversible and non-reversible Markov chain Monte Carlo algorithms for reservoir simulation problems

2020

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We compare numerically the performance of reversible and non-reversible Markov Chain Monte Carlo algorithms for high dimensional oil reservoir problems; because of the nature of the problem at hand, the target measures from which we sample are supported on bounded domains. We compare two strategies to deal with bounded domains, namely reflecting proposals off the boundary and rejecting them when they fall outside of the domain. We observe that for complex high dimensional problems reflection mechanisms outperform rejection approaches and that the advantage of introducing non-reversibility in the Markov Chain employed for sampling is more and more visible as the dimension of the parameter space increases.

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Piecewise deterministic Markov processes for scalable Monte Carlo on restricted domains

Cited by 51 publications

References 25 publications

Event-chain Monte Carlo with factor fields

Event-chain Monte Carlo with factor fields

JeLLyFysh-Version1.0 — a Python application for all-atom event-chain Monte Carlo

Reversible and non-reversible Markov chain Monte Carlo algorithms for reservoir simulation problems

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