Preserving correlations between trajectories for efficient path sampling.

Area of Science:

• Statistical Mechanics
• Computational Physics
• Complex Systems

Background:

• Importance sampling is crucial for unbiased exploration of rare dynamical behaviors in complex systems.
• Efficient sampling requires balancing substantial pathway changes with reasonable acceptance rates, a challenge for long, chaotic trajectories.

Purpose of the Study:

• To examine schemes for improving trajectory sampling in complex systems, particularly for long trajectories with chaotic dynamics.
• To identify sampling strategies that can scale effectively to long trajectories using a modern Markov chain Monte Carlo perspective.

Main Methods:

• Analysis of trajectory sampling schemes, including those using artificial forces to correlate trial and reference paths.
• Application of non-equilibrium statistical mechanics principles to Markov chain Monte Carlo sampling.
• Investigation of "noise guidance" strategies that manipulate random number sequences for stochastic time evolution.

Main Results:

• Identified "noise guidance" as a promising strategy for scaling trajectory sampling to long trajectories.
• Demonstrated that effective noise guidance can synchronize trajectories, enabling efficient path sampling.
• Showcased successful application in the Glauber dynamics of a two-dimensional Ising model.

Conclusions:

• "Noise guidance" by manipulating random number sequences is a key strategy for efficient path sampling of long trajectories.
• This approach overcomes challenges posed by chaotic dynamics in complex systems.
• Efficient path sampling is achievable even for very long trajectories when noise guidance synchronizes dynamics effectively.