Department of Physics, Duke University, Durham, North Carolina 27708, USA.
Laboratoire de Physique Théorique et Modèles Statistiques, Université Paris-Sud, CNRS UMR 8626, 91405 Orsay Cedex, France.
Phys Rev E. 2018 Jan;97(1-1):010104. doi: 10.1103/PhysRevE.97.010104.
We introduce and apply an efficient method for the precise simulation of stochastic dynamical processes on locally treelike graphs. Networks with cycles are treated in the framework of the cavity method. Such models correspond, for example, to spin-glass systems, Boolean networks, neural networks, or other technological, biological, and social networks. Building upon ideas from quantum many-body theory, our approach is based on a matrix product approximation of the so-called edge messages-conditional probabilities of vertex variable trajectories. Computation costs and accuracy can be tuned by controlling the matrix dimensions of the matrix product edge messages (MPEM) in truncations. In contrast to Monte Carlo simulations, the algorithm has a better error scaling and works for both single instances as well as the thermodynamic limit. We employ it to examine prototypical nonequilibrium Glauber dynamics in the kinetic Ising model. Because of the absence of cancellation effects, observables with small expectation values can be evaluated accurately, allowing for the study of decay processes and temporal correlations.
我们介绍并应用了一种有效的方法，用于精确模拟局部树状图上的随机动力过程。在腔方法的框架内处理具有循环的网络。例如，此类模型对应于自旋玻璃系统、布尔网络、神经网络或其他技术、生物和社交网络。基于量子多体理论的思想，我们的方法基于所谓的边消息——顶点变量轨迹条件概率的矩阵乘积逼近。通过控制矩阵乘积边消息（MPEM）截断中的矩阵维度，可以调整计算成本和准确性。与蒙特卡罗模拟相比，该算法具有更好的误差缩放特性，适用于单实例和热力学极限。我们将其应用于研究动力学伊辛模型中的典型非平衡 Glauber 动力学。由于不存在抵消效应，可以准确评估具有小期望值的可观测量，从而可以研究衰减过程和时间相关性。
