标题：A mean-field opinion model on hypergraphs: From modeling to inference
报告时间：2024年06月21日（星期五）15:30-16:30
报告地点：人民大街校区数学与统计学院二楼会议室
主讲人：褚伟奇
主办单位：数学与统计学院
报告内容简介：
The perspectives and opinions of people change and spread through social interactions on a daily basis. In the study of opinion dynamics, one often models social entities (such as Facebook accounts) as nodes and their relationships (such as friendships) as edges, and examines how opinions evolve as dynamical processes on networks, including graphs, hypergraphs, multi-layer networks, etc. In the first part of my talk, I will introduce a model of opinion dynamics and derive its mean-field limit as the total number of agents goes to infinity. The mean-field opinion density satisfies a kinetic equation of Kac type. We prove properties of the solution of this equation, including nonnegativity, conservativity, and steady-state convergence. The parameters of such opinion models play a nontrivial role in shaping the dynamics and can also be in the form of functions. In reality, it is often impractical to measure these parameters directly. In the second part of the talk, I will approach the problem from an inverse perspective and present how to infer the parameters from limited partial observations. I will provide sufficient conditions of measurement for two scenarioses, such that one is able to identify the parameters uniquely. I will also provide a numerical algorithm of the inference when the data set only has a limited number of data points.
主讲人简介：
褚伟奇，2014年学士毕业于北京大学，2019年博士毕业于美国宾夕法尼亚州立大学，2019-2023年在美国加州大学洛杉矶分校任访问助理教授，于2023年入职美国马萨诸塞大学-阿默斯特分校任助理教授。研究方向为多尺度建模，数据科学，动力系统和网络科学。
