Efficient generation of barrier crossing trajectories using approximate Brownian bridges

Area of Science:

• Stochastic processes
• Computational physics
• Chemical kinetics

Background:

• Barrier crossing events are often rare and computationally challenging to simulate.
• Existing methods for sampling these events can suffer from inefficiency or accumulating errors.
• Accurate simulation of rare events is vital for understanding complex systems.

Purpose of the Study:

• To develop an efficient and accurate method for generating stochastic trajectories conditioned on barrier crossing.
• To provide a robust technique for sampling rare events in systems with potential energy barriers.
• To enable more effective simulation of complex chemical and physical processes.

Main Methods:

• Utilizing a Brownian bridge technique to generate conditioned random walks.
• Deriving a one-dimensional approximation for the hitting probability (committer function) using asymptotic methods.
• Applying importance sampling with the approximate solution for enhanced sampling efficiency.

Main Results:

• The derived approximation for the committer function is analytically simple and accurate for increasing barrier heights.
• Brownian bridge trajectories generated with the approximation yield accurate conditional statistics.
• The method demonstrates effectiveness in simulating rare events in the Schögl reaction network.

Conclusions:

• The developed methodology offers a highly efficient approach for simulating rare barrier crossing events.
• This technique significantly reduces computational cost and error accumulation in sampling rare events.
• The approach holds broad applicability for simulating rare events across diverse physical and chemical systems.