Accelerated Jarzynski Estimator with Deterministic Virtual Trajectories
This incremental improvement addresses a bottleneck in statistical physics and machine learning for researchers using partition function estimation.
The paper tackles the slow convergence of the Jarzynski estimator for partition functions by introducing deterministic virtual trajectories in augmented state space, achieving second-order acceleration and outperforming conventional methods in numerical experiments on multimodal distributions.
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 the simulated Langevin dynamics through the Jarzynski equality. However, the original estimator suffers from 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 the Hamiltonian dynamics. We theoretically show that our approach achieves second-order acceleration compared to a naive estimator with the Langevin dynamics and zero variance estimation on harmonic potentials. We also present numerical experiments on three multimodal distributions and a practical example where the proposed method outperforms the conventional method, and provide theoretical explanations.