Accurately modeling human mobility is critical for urban planning, epidemiology, and traffic management. In this work, we introduce Markovian Reeb Graphs, a novel framework for simulating spatiotemporal trajectories that preserve Patterns of Life (PoLs) learned from baseline data. By combining individual- and population-level mobility structures within a probabilistic topological model, our approach generates realistic future trajectories that capture both consistency and variability in daily life. Evaluations on the Urban Anomalies dataset (Atlanta and Berlin subsets) using the Jensen-Shannon Divergence (JSD) across population- and agent-level metrics demonstrate that the proposed method achieves strong fidelity while remaining data- and compute-efficient. These results position Markovian Reeb Graphs as a scalable framework for trajectory simulation with broad applicability across diverse urban environments.

翻译：准确建模人类移动性对于城市规划、流行病学和交通管理至关重要。本文提出马尔可夫Reeb图这一新颖框架，用于模拟时空轨迹，同时保持从基准数据中学习到的生活模式。通过将个体层面与群体层面的移动结构结合到概率拓扑模型中，我们的方法能够生成捕捉日常生活一致性与变异性的真实未来轨迹。基于Urban Anomalies数据集（亚特兰大和柏林子集）的评估表明，采用群体层面与个体层面指标的Jensen-Shannon散度进行度量时，所提方法在保持数据与计算高效性的同时实现了强保真度。这些结果确立了马尔可夫Reeb图作为可扩展轨迹模拟框架的潜力，在多样化城市环境中具有广泛适用性。