重要抽样在非平衡过程大偏差计算中的应用

Adaptive sampling of large deviations

We introduce and test an algorithm that adaptively estimates large deviation functions characterizing the fluctuations of additive functionals of Markov processes in the long-time limit. These functions play an important role for predicting the probability and pathways of rare events in stochastic processes, as well as for understanding the physics of nonequilibrium systems driven in steady states by external forces and reservoirs. The algorithm uses methods from risk-sensitive and feedback control to estimate from a single trajectory a new process, called the driven process, known to be effic…

Optimal sampling of dynamical large deviations via matrix product states

The large deviation (LD) statistics of dynamical observables is encoded in the spectral properties of deformed Markov generators. Recent works have shown that tensor network methods are well suited to compute the relevant leading eigenvalues and eigenvectors accurately. However, the efficient generation of the corresponding rare trajectories is a harder task. Here we show how to exploit the MPS approximation of the dominant eigenvector to implement an efficient sampling scheme which closely resembles the optimal (so-called "Doob") dynamics that realises the rare events. We demonstrate our appr…

Efficient large deviation estimation based on importance sampling

We present a complete framework for determining the asymptotic (or logarithmic) efficiency of estimators of large deviation probabilities and rate functions based on importance sampling. The framework relies on the idea that importance sampling in that context is fully characterized by the joint large deviations of two random variables: the observable defining the large deviation probability of interest and the likelihood factor (or Radon-Nikodym derivative) connecting the original process and the modified process used in importance sampling. We recover with this framework known results about …

非平衡稳态中大偏差的重要性抽样。I

Importance sampling large deviations in nonequilibrium steady states. I

大偏差函数包含关于驱动到非平衡稳态的系统的稳定性和响应的信息，并且以这种方式类似于平衡系统的自由能。与平衡自由能一样，除了最简单的系统之外，用数值计算大偏差函数是困难的，因为它们的构造依赖于指数罕见事件。在这一系列的第一篇论文中，我们评估了不同的基于概率的采样方法，能够计算大偏差函数的时间综合观测值在非平衡稳态。我们说明了一些收敛的标准和最佳做法，使用一些不同的模型，包括有偏见的布朗步行，驱动格子气，和自组装模型。我们展示了两种流行的采样轨迹合奏，过渡路径采样和扩散蒙特卡罗方法，遭受指数发散的相关性在轨迹空间中作为偏置参数的函数时，估计大偏差函数。提高这些算法的效率，需要引入的轨迹的指导功能。

Probing the large deviations of the Kardar-Parisi-Zhang equation at short time with an importance sampling of directed polymers in random media

The one-point distribution of the height for the continuum Kardar-Parisi-Zhang (KPZ) equation is determined numerically using the mapping to the directed polymer in a random potential at high temperature. Using an importance sampling approach, the distribution is obtained over a large range of values, down to a probability density as small as $10^{-1000}$ in the tails. The short time behavior is investigated and compared with recent analytical predictions for the large-deviation forms of the probability of rare fluctuations, showing a spectacular agreement with the analytical expressions. The …

对偶因子图上的一种重要性抽样方案。I.强外场模型

An Importance Sampling Scheme on Dual Factor Graphs. I. Models in a Strong External Field

我们提出了一个重要性抽样方案来估计二维铁磁Ising模型和二维铁磁$q$ -态Potts模型的配分函数，这两个模型都是在外部磁场的存在下。该方案在对偶Forney因子图中运行，并且能够有效地计算在宽范围的模型参数下的配分函数的估计。特别是，我们考虑的模型是在一个强大的外部磁场。