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Cool walking: a new Markov chain Monte Carlo sampling method.

Scott Brown1, Teresa Head-Gordon

  • 1Department of Bioengineering, University of California, Berkeley, CA 94720, USA.

Journal of Computational Chemistry
|December 17, 2002
PubMed
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Cool Walking (C-Walking) is a novel simulation technique for enhanced sampling in complex systems. This method improves upon existing algorithms by using tandem Markov chains at different temperatures to efficiently cross energy barriers.

Area of Science:

  • Computational Physics
  • Statistical Mechanics
  • Materials Science

Background:

  • Effective relaxation processes in complex systems like proteins and spin glasses necessitate specialized simulation techniques for barrier crossing and ergodic sampling.
  • Existing methods, including Metropolis Monte Carlo (MMC) adaptations, Hybrid Monte Carlo (HMC), Jump Walking (J-Walking), Smart Walking (S-Walking), Smart Darting, and Parallel Tempering, aim to improve sampling efficiency but face limitations.

Purpose of the Study:

  • To introduce and evaluate Cool Walking (C-Walking), a new simulation technique designed to enhance sampling efficiency in difficult systems.
  • To demonstrate C-Walking's ability to ensure ergodic sampling by facilitating barrier crossing.

Main Methods:

  • C-Walking propagates two Markov chains in tandem: one at a high (ergodic) temperature and another at a low temperature.

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  • Nonlocal trial moves for the low-temperature walker are generated by sampling from the high-temperature distribution followed by a statistical quenching process.
  • The method incorporates optimizations such as attempting jumps at intermediate temperatures and utilizing "windows" of states to reduce cooling steps and improve acceptance ratios.

    • Main Results:

    • C-Walking requires only one high-temperature walker and satisfies detailed balance.
    • The tandem propagation of walkers minimizes sampling degradation due to correlations.
    • Comparisons on a one-dimensional rugged potential energy surface show C-Walking exhibits superior sampling efficiency compared to J-Walking, S-Walking, Smart Darting, and Parallel Tempering, as assessed by two ergodic measures.

    Conclusions:

    • C-Walking offers a practical and efficient alternative for achieving ergodic sampling in complex systems.
    • The method's design, including tandem walkers and optimized cooling steps, leads to superior performance in overcoming energy barriers.
    • C-Walking presents a promising advancement for simulations requiring robust barrier-crossing capabilities.