Accelerated Jarzynski Estimator with Deterministic Virtual Trajectories

The Jarzynski estimator is a powerful tool that uses nonequilibrium statistical physics to numerically obtain partition functions of probability distributions. The estimator reconstructs partition functions with trajectories of simulated Langevin dynamics through the Jarzynski equality. However, the original estimator suffers from its slow convergence because it depends on rare trajectories of stochastic dynamics. In this paper we present a method to significantly accelerate the convergence by introducing deterministic virtual trajectories generated in augmented state space under Hamiltonian dynamics. We theoretically show that our approach achieves second-order acceleration compared to a naive estimator with Langevin dynamics and zero variance estimation on harmonic potentials. Moreover, we conduct numerical experiments on three multimodal distributions where the proposed method outperforms the conventional method, and provide theoretical explanations.