确定性虚拟轨迹加速Jarzynski估计
Accelerated Jarzynski Estimator with Deterministic Virtual Trajectories
摘要：
Jarzynski估计量是一个强大的工具，它使用非平衡统计物理来数值地获得概率分布的配分函数。该估计器通过Jarzynski等式用模拟的Langevin动力学轨迹重构配分函数。然而，原始估计的收敛速度慢，因为它依赖于随机动力学的罕见轨迹。在本文中，我们提出了一种方法，显着加快收敛，通过引入确定性的虚拟轨迹产生的增广状态空间下的哈密顿动力学。我们从理论上表明，我们的方法实现了二阶加速相比，一个天真的估计与朗之万动力学和零方差估计谐波电位。我们还提出了三个多峰分布的数值实验和一个实际的例子，所提出的方法优于传统的方法，并提供理论解释。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
