本文提出一种计算框架，通过将拓扑数据分析（Topological Data Analysis, TDA）与方程自由法（Equation-Free Method）相结合，探索并分析复杂基于智能体的网络模型的宏观动力学行为。为验证该方法的有效性，我们将其应用于Erdős–Rényi型随机网络。本方法的核心是基于TDA的滤波过程，该过程以激活网络节点（即智能体）的密度为驱动变量，并从中提取一个粗粒化的宏观拓扑可观测量；该可观测量由持续同调Betti数定义，从而在显著降低数据维度的同时保留关键拓扑特征。随后，在方程自由法框架下，我们首先证明可利用拓扑性质实现\textit{提升过程}（lifting procedure），其次构建一个数据驱动的演化律，用以刻画该宏观变量的动力学行为。最后，我们开展数值分岔与稳定性分析，以探究所涌现宏观动力学的整体行为及其定性转变。

In this work, we present a computational framework for exploring and analyzing the macroscopic dynamics of complex agent-based network models by integrating Topological Data Analysis with the Equation-Free Method. To demonstrate the effectiveness of our method, we apply it to Erdős--Rényi-type random networks. Central to our approach is a Topological Data Analysis-based filtration process driven by the density of activated network nodes (agents), from which we extract a coarse-grained macroscopic topological observable. This observable is defined via persistent Betti numbers, thus requiring significantly reduced data dimensionality while retaining essential topological features. Subsequently, within the Equation-Free Method framework, we show firstly that a \textit{lifting procedure} can be achieved using topological properties and secondly, a data-driven evolution law that governs the dynamics of this macroscopic variable. Finally, we perform a numerical bifurcation and stability analysis to investigate the global behavior and qualitative transitions of the emergent macroscopic dynamics.