Estimating the speed-up of Adaptively Restrained Langevin Dynamics

We consider Adaptively Restrained Langevin dynamics, in which the kinetic energy function vanishes for small velocities. Properly parameterized, this dynamics makes it possible to reduce the computational complexity of updating inter-particle forces, and to accelerate the computation of ergodic averages of molecular simulations. In this paper, we analyze the influence of the method parameters on the total achievable speed-up. In particular, we estimate both the algorithmic speed-up, resulting from incremental force updates, and the influence of the change of the dynamics on the asymptotic variance. This allows us to propose a practical strategy for the parametrization of the method. We validate these theoretical results by representative numerical experiments.