Efficient dynamic importance sampling of rare events in one dimension

Area of Science:

• Computational physics
• Chemical kinetics
• Stochastic processes

Background:

• Stochastic path-integral theory provides a framework for analyzing complex systems.
• Efficient computation of reaction rates is crucial for understanding chemical and physical processes.
• Bistable systems exhibit complex dynamics, making rate calculations challenging.

Purpose of the Study:

• To improve the efficiency of reaction rate computations in one-dimensional, bistable, overdamped stochastic systems.
• To compare the performance of dynamic importance sampling (DIMS) methods against unbiased simulations.
• To quantify the efficiency gains achieved by DIMS for varying energy barrier heights.

Main Methods:

• Utilizing stochastic path-integral theory and simulation techniques.
• Implementing and evaluating various dynamic importance sampling (DIMS) algorithms.
• Comparing DIMS performance against unbiased simulation using a defined efficiency measure.
• Generating artificial crossing events via the Onsager-Machlup action's closed-form solution.

Main Results:

• DIMS methods demonstrated significant efficiency improvements over unbiased simulations.
• Efficiency gains reached factors of approximately 20 for a 5k(B)T barrier and 300 for a 9k(B)T barrier.
• The gains are attributed to emulating natural crossing events with reduced waiting times, corrected for in rate calculations.
• Methods requiring only the first derivative of the potential performed nearly as well as those using the second derivative.

Conclusions:

• Dynamic importance sampling offers substantial computational advantages for reaction rate calculations in stochastic systems.
• The efficiency gains are particularly pronounced for systems with higher energy barriers.
• The study highlights the utility of one-dimensional models and suggests potential extensions to higher-dimensional systems.