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San Francisco's Golden Gate Bridge is exposed to temperatures ranging from -15 °C to 40 °C. At its coldest, the main span of the bridge is 1275 m long. Assuming that the bridge is made entirely of steel, what is the change in its length between these temperatures?
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Annealed importance sampling with constant cooling rate.

Edoardo Giovannelli1, Gianni Cardini1, Cristina Gellini1

  • 1Dipartimento di Chimica, Università di Firenze, Via della Lastruccia 3, I-50019 Sesto Fiorentino, Italy.

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Summary
This summary is machine-generated.

Annealed importance sampling (AIS) provides a robust method for calculating averages from simulated annealing trajectories. This review connects AIS to nonequilibrium methods and suggests optimal cooling schedules for improved performance.

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Area of Science:

  • Computational Physics
  • Statistical Mechanics
  • Simulation Methods

Background:

  • Annealed importance sampling (AIS) is a simulation technique developed by Neal for weighting configurations from simulated annealing.
  • It enables computation of equilibrium averages using weighted averages of final configurations from annealed trajectories.

Purpose of the Study:

  • To review annealed importance sampling (AIS) from the perspective of nonequilibrium path-ensemble averages.
  • To demonstrate the generality of AIS beyond thermal protocols.
  • To identify optimal temperature schedules for enhanced performance.

Main Methods:

  • Review of existing literature on annealed importance sampling (AIS).
  • Comparison of AIS with nonequilibrium path-ensemble averages (Crooks' method).
  • Analysis of different temperature schedules (constant cooling rate vs. stepwise).

Main Results:

  • Equivalence established between Neal's AIS and Crooks' nonequilibrium treatments.
  • Constant cooling rate schedules are shown to outperform stepwise cooling.
  • Increasing intermediate temperatures generally improves AIS performance for a fixed computation time.

Conclusions:

  • AIS is a versatile method applicable to various protocols, not just thermal ones.
  • Optimized temperature schedules, particularly constant cooling rates, enhance the efficiency of AIS.
  • Further improvements in AIS performance can be achieved by increasing the number of intermediate temperatures.