多正则反馈控制的种群动力学方法
Population dynamics method with a multi-canonical feedback control
摘要：
我们讨论了Giardinà-Kurchan-Peliti人口动力学方法，用于评估马尔可夫过程中时间平均量的大偏差[Phys. Rev. Lett. \textbf{96}，120603（2006）]。该方法表现出在某些情况下可能很大的系统误差，特别是对于具有弱噪声、具有多个自由度或接近动态相变的系统。我们展示了如何通过在算法中引入控制力来减轻这些错误。这些力量是由一个迭代和反馈计划，启发在平衡采样的multicanonical方法。我们在一个简单的模型中展示了大幅改善的结果，并讨论了更复杂系统的潜在应用。
英文摘要：
We discuss the Giardinà-Kurchan-Peliti population dynamics method for evaluating large deviations of time averaged quantities in Markov processes [Phys. Rev. Lett. \textbf{96}, 120603 (2006)]. This method exhibits systematic errors which can be large in some circumstances, particularly for systems with weak noise, with many degrees of freedom, or close to dynamical phase transitions. We show how these errors can be mitigated by introducing control forces within the algorithm. These forces are determined by an iteration-and-feedback scheme, inspired by multicanonical methods in equilibrium sampling. We demonstrate substantially improved results in a simple model and we discuss potential applications to more complex systems.
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