Variance-reduced random batch Langevin dynamics

The random batch method is advantageous in accelerating force calculations in particle simulations, but it poses a challenge of removing the artificial heating effect in application to the Langevin dynamics. We develop an approach to solve this issue by estimating the force variance, resulting in a variance-reduced random batch Langevin dynamics. Theoretical analysis shows the high-order local truncation error of the time step in the numerical discretization scheme, consistent with the fluctuation-dissipation theorem. The numerical results indicate that the method can achieve a significant variance reduction since a smaller batch size provides accurate approximation, demonstrating the attractive feature of the variance-reduced random batch method for Langevin dynamics.