《科学大讲堂 第260期》段金桥 讲席教授：随机动力系统中的临界迁移：从最可能路径到薛定谔桥

以下内容根据公开信息整理，并经大模型处理生成，可能存在疏漏或误差，请以实际信息为准。

• 题目: 随机动力系统中的临界迁移：从最可能路径到薛定谔桥
• 主讲人：段金桥 讲席教授 @ 大湾区大学
• 时间：2026年10月29日 16:00-17:00
• 地点：理学院一楼化学系C1038报告厅

主讲人简介

Jinqiao Duan is Chair Professor of Mathematics at Great Bay University in Dongguan, Guangdong Province, China. He is an expert in stochastic dynamical systems and stochastic partial differential equations, with a focus on critical transitions in biophysical and geophysical systems. He received his BS from Wuhan University, his MS from the Chinese Academy of Sciences, and his PhD from Cornell University, followed by postdoctoral research at the California Institute of Technology. Before joining Great Bay University, Professor Duan served as a professor in the United States for over two decades. His academic leadership roles include serving as Associate Director of the NSF Institute for Pure and Applied Mathematics (IPAM) at UCLA, and Rotating Director for the NSF Institute for Data, Econometrics, Algorithms, and Learning (IDEAL). He was also offered the Gary Havener Department Chair at the Missouri University of Science and Technology. Professor Duan was awarded the Young Scientist’s Publication Award in Nonlinear Science by the European Geophysical Society. He is the author of An Introduction to Stochastic Dynamics (Cambridge University Press, 2015), co-author of Effective Dynamics of Stochastic Partial Differential Equations (with Wei Wang; Elsevier, 2014), and co-author of Geometric Methods for Stochastic Dynamical Systems (with Ting Gao, Qiao Huang and Yuanfei Huang; Springer, 2026).

讲座简介

The interplay between nonlinearity and uncertainty can give rise to abrupt, critical transitions between qualitatively distinct dynamical regimes. Understanding these phenomena requires mathematical frameworks capable of connecting metastable states, evolving probability distributions, and finite-time transition dynamics. In this talk, I will review several complementary approaches to modeling critical transitions in stochastic dynamical systems, including connecting orbits, most probable transition paths derived from Onsager–Machlup action functionals, probability density evolution, and Schrödinger bridge problems. I will highlight the structural relationships among these formulations and contrast the distinct information each provides about metastable switching. Building on these foundations, I will examine topological, probabilistic, variational, and analytical indicators used to detect, characterize, and anticipate sudden regime shifts. Finally, I will address the open problem of transition-path selection: among multiple dynamically admissible pathways, what determines which trajectories dominate over a prescribed finite time horizon? Key concepts will be illustrated using representative examples of stochastic dynamical systems.

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