近年来，复杂网络已成为统计物理及其交叉学科研究的一个热点。复杂网络拓扑和动力学行为演化涉及微观、介观，乃至宏观的多个时间和空间拓扑尺度。微观模拟适用尺度相对较小，宏观唯象理论（如平均场方法）又缺乏对微观机制的理解，因此需要发展有效的多尺度理论方法。目前复杂网络上多尺度粗粒化方法研究取得了进展，但面临两个问题：一是不能有效解决动力学时间多尺度问题，二是对于关联较强或高度复杂网络，如最近报道的网络的网络、多层网络等也有局限。本项目拟运用统计力学原理，建立复杂网络上高阶近似下多尺度动力学粗粒化、杂化多尺度粗粒化和时空粗粒化理论与模拟方法，实现不同尺度理论方法的有机衔接；开发相应的计算程序；研究复杂网络上平衡和非平衡相变、临界现象、涨落、尺度效应以及同步、病毒传播的动力学规律，从而揭示介观乃至宏观现象的微观机理和调控机制，为深入理解复杂网络上多尺度动力学过程与拓扑结构之间的深层次联系提供新的启示。

Recently, complex network has been one of the most active research topics in statistical physics and closely related disciplines. The dynamics of network and its topology usually associate with multiscale processes spanning from microscopic to mesoscopic, and to macroscopic level. It is known that brute-force simulations are quite expensive and sometimes even become impossible. While phenomenological models, such as mean-field description, may capture certain properties of the system, but often ignore microscopic details and fluctuation effects that may be important near critical points. Therefore a promising way is to develop multiscale theory and approaches, aiming at significantly reducing the degree of freedom while properly preserving the microscopic information of interest. Now, several coarse-grained methods to multiscale dynamics of complex network have been proposed, however these methods can not deal with the multiscale problem of dynamics evolution. In addition, there are also some limits in coping with the strongly correlated network or highly complex network, for instance, network of network, multiplex network and so on. In this proposal, we will apply the statistical mechanics theory to develop mesoscopic approaches on complex networks, including coarse-grained method to multiscale dynamics based on high order approximation, hybrid multiscale coarse-grained method and spatiotemporal coarse-grained method, and bridge the gap between the microscopic details and system level behaviors. We will design a series of computer programs and perform extensive numerical simulations on different network topologies to study the equilibrium and nonequilibrium phase transition, fluctuations, finite-size effects, synchronization and epidemic spreading dynamics. Our study may provide a new perspective and approach to understand the underlying mechanism between multiscale dynamics and network topology.