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Extended state-space Monte Carlo methods.

S B Opps1, J Schofield

  • 1Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario, Canada M5S 3H6.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 21, 2001
PubMed
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This study enhances parallel-tempering algorithms for rough energy landscapes. Deterministic methods were explored but found not to improve sampling rates over standard parallel tempering.

Area of Science:

  • Computational Physics
  • Statistical Mechanics
  • Monte Carlo Methods

Background:

  • Parallel-tempering algorithms are used to improve sampling in systems with complex energy landscapes.
  • A drawback of parallel tempering is the stochastic nature of auxiliary variable dynamics.
  • Quasiergodic sampling can be a challenge in systems with rough energy landscapes.

Purpose of the Study:

  • To develop and analyze extensions of the parallel-tempering algorithm.
  • To investigate deterministic methods for improving sampling mobility in extended state spaces.
  • To compare the efficiency of deterministic methods against standard parallel tempering.

Main Methods:

  • Coupling individual Monte Carlo chains to form composite chains.
  • Extending the state space with parameters to enhance sampling mobility.

Related Experiment Videos

  • Developing statistical quenching and heating procedures, analogous to simulated annealing.
  • Testing methods on a two-dimensional spin (xy) model and a polypeptide system.

    • Main Results:

    • The net mobility of coupled chains depends on coupling time and distribution overlap.
    • Optimal sampling conditions were found by attempting configuration swaps after few Monte Carlo updates.
    • Deterministic procedures did not yield improved sampling rates compared to parallel tempering.

    Conclusions:

    • Extensions to parallel-tempering algorithms were developed and analyzed.
    • Deterministic methods for parameter space exploration do not outperform standard parallel tempering.
    • Efficient parallel tempering involves frequent configuration swap attempts.