学术报告报告主题: Beyond Distance: Quantifying Point Cloud Dynamics with Persistent Homology and Dynamic Optimal Transport
报 告 人: 高婷 副教授（华中科技大学）
报告时间： 2026年3月22日（星期日）上午11:10-12:00
报告地点： 37号楼（清清文理楼）3A02
邀 请 人: 刘锐 教授、陈培 教授
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数学学院
2026年3月16日
报告摘要：
We introduce a framework for analyzing topological tipping in time evolutionary point clouds by extending the recently proposed Topological Optimal Transport (TpOT) distance. While TpOT unifies geometric, homological and higher‐order relations into one metric, its global scalar distance can obscure transient, localized structural reorganizations during dynamic phase transitions. To overcome this limitation, we present a hierarchical dynamic evaluation framework driven by a novel topological and hypergraph reconstruction strategy. Instead of directly interpolating abstract network parameters, our method interpolates the underlying spatial geometry and rigorously re-computes the valid topological structures, ensuring physical fidelity. Along this geodesic, we introduce a set of multi-scale indicators: macroscopic metrics (Topological Distortion and Persistence Entropy) to capture global shifts, and a novel mesoscopic dual-perspective Hypergraph Entropy (node-perspective and edge-perspective) to detect highly sensitive, asynchronous local rewirings. We further propagate the cycle-level entropy change onto individual vertices to form a point-level topological field. Extensive evaluations on physical dynamical systems (Rayleigh-Van der Pol limit cycles, Double-Well cluster fusion), high-dimensional biological aggregation (D'Orsogna model), and longitudinal stroke fMRI data demonstrate the utility of combining transport‐based alignment with multi‐scale entropy diagnostics for dynamic topological analysis.
报告人介绍：
华中科技大学数学与统计学院、数学中心副教授。2015年毕业于伊利诺伊理工大学，获博士学位。曾在美国社交网络公司Twitter(推特)担任高级数据科学家和机器学习算法工程师，开发基于深度强化学习和在线深度学习的推荐系统及在线学习的实时竞价系统，解决了实际产品线中的模型稳健性、准确度、数据选择偏差等技术难题。现主要研究非高斯随机动力系统的辨识、有效动力学预测与最优控制，及在脑科学、信息通信与金融中的应用。在SIAM、AMM等期刊发表SCI论文40余篇。主持国家自然科学基金青年项目，骨干参与基金委重点专项、科技部重大项目、国际创新研究团队项目，广东省动力系统与神经系统重点实验室等。