复杂系统的高维混沌时间序列分析与预测研究

Complex systems with chaotic characteristics exist in various natural fields. Research on observed chaotic time series has gradually become the primary means for studying the complex systems and it is helpful to reveal the operation mechanism of the complex systems. With the development of information technology, the chaotic time series observed from complex systems, such as meteorology, environment and ocean system, show high-dimensional, time-varying and large-sample characteristics, which put forward higher demand for analysis and modeling of complex systems. This project spreads out from the four following respects: 1) We study the correlation and causality analysis methods of high-dimensional chaotic time series, determine the relationship between influencing variables of complex systems, and provide theoretical basis for predicting and modeling; 2) Aiming at the chaotic time series with time-varying characteristics, we propose an online learning method for dynamic environment and large sample data, which is used to forecast the trend of complex system in real time; 3) We establish the deep neural networks to extract the effective characteristics of massive high-dimensional chaotic time series, and introduce the feedback mechanism to describe the sequential characteristic of time series; 4) We research the optimization method, which can optimize the process of selecting input variables, model structures and parameters, and finally improve the prediction accuracy. This project presents new ideas for chaotic time series analysis and modeling, which can be used to predict and control the actual complex systems, and then realize advanced prediction and assistant decision.

具有混沌特性的复杂系统广泛存在于自然界的各个领域，通过对观测到的混沌时间序列进行研究，有助于揭示复杂系统的运行机理，逐渐成为研究复杂系统的主要手段。随着信息技术的发展，从气象、环境、海洋等复杂系统观测到的混沌时间序列呈现出高维、时变、大样本等新的特性，对复杂系统的分析与建模提出了更高的要求。本项目拟从以下四个方面展开研究：1）研究高维混沌时间序列的相关性与因果分析，确定复杂系统影响变量间的相互关系，为预测建模提供理论依据；2）针对具有时变特性的混沌时间序列，提出适用于动态变化环境和大样本数据的在线学习方法，实时预测复杂系统的变化趋势；3）建立深度神经网络，提取海量高维混沌时间序列的有效特征，并引入反馈机制描述其时序特征；4）研究优化方法，实现输入变量选择、模型结构和参数优化，提高预测准确性。本项目提出混沌时间序列分析与建模的新思路，对实际复杂系统进行预测和调控，实现前瞻预报与辅助决策。

本项目研究具有高维、时变、大样本等特性的混沌时间序列，实现气象、环境、海洋等复杂系统的分析与建模，探究复杂系统的运行机理和发展趋势。本项目从以下四个方面展开研究：1）挖掘高维混沌时间序列的潜在信息，建立因果关系网络；2）研究在线学习方法，实时预测混沌时间序列变化趋势；3）针对海量高维混沌时间序列，建立深度反馈神经网络；4）研究优化方法，优化模型输入变量、结构和参数。在基金的资助下，项目组发表高水平期刊论文27篇、国际会议论文12篇。代表性研究成果发表于国际顶级期刊IEEE Transactions on Neural Networks and Learning Systems、IEEE Transactions on Cybernetics、IEEE Transactions on Knowledge and Data Engineering等和国内知名期刊《自动化学报》等上。项目组申请发明专利5项，其中授权专利1项、公开专利4项。此外，项目组培养了博士生6名、硕士生12名。本项目的研究方法是复杂系统分析与建模的重要手段，具有广阔的应用前景。