Variance-reduced random batch Langevin dynamics.

Area of Science:

• Computational physics
• Molecular dynamics simulations

Background:

• The random batch method accelerates particle simulations but introduces artificial heating in Langevin dynamics.
• Addressing this heating effect is crucial for accurate simulation results.

Purpose of the Study:

• To develop a variance-reduced random batch Langevin dynamics method.
• To eliminate the artificial heating effect caused by the random batch approach.

Main Methods:

• Estimating the force variance to reduce fluctuations.
• Implementing a variance-reduced random batch Langevin dynamics algorithm.
• Theoretical analysis of local truncation error and consistency with the fluctuation-dissipation theorem.

Main Results:

• The proposed method effectively reduces variance in Langevin dynamics.
• Smaller batch sizes provide accurate approximations, demonstrating efficiency.
• Theoretical analysis confirms high-order local truncation error.

Conclusions:

• The variance-reduced random batch method is an effective solution for artificial heating in Langevin dynamics.
• This method offers accurate and efficient particle simulations.
• It presents an attractive feature for advanced computational physics applications.