科学与工程计算系列讨论班——Detecting early-warning signals of critical distribution-transition for nonlinear dynamical systems (基于大数据的临界检测理论和方法)
主 题: 科学与工程计算系列讨论班——Detecting early-warning signals of critical distribution-transition for nonlinear dynamical systems (基于大数据的临界检测理论和方法)
报告人: Luonan Chen (陈洛南), (Key Laboratory of Systems Biology, Chinese Academy of Sciences)
时 间: 2016-11-02 10：30-11：30
地 点: 理科一号楼 1114
Identifying early-warning signals of a critical transition for a complex system is difficult, especially when the target system is constantly perturbed by big noise, which makes the traditional methods fail due to the strong fluctuations of the observed data. In this work, we show that the critical transition is not traditional state-transition but probability distribution-transition when the noise is not sufficiently small, which, however, is a ubiquitous case in real systems. We present a model-free computational method to detect the warning signals before such transitions. The key idea behind is a strategy: “making big noise smaller” by a distribution-embedding scheme, which transforms the data from the observed state-variables with big noise to their distribution-variables with small noise, and thus makes the traditional criteria effective because of the significantly reduced fluctuations. Specifically, increasing the dimension of the observed data by moment expansion that changes the system from state-dynamics to probability distribution-dynamics, we derive new data in a higher dimensional space but with much smaller noise. Then, we develop a criterion based on the dynamical network marker (DNM) to signal the impending critical transition using the transformed higher dimensional data. We also demonstrate the effectiveness of our method in biological, ecological and financial systems.