在線學術報告 | 盧飛副教授：相互作用粒子系統的統計學習和逆問題

Systems of interacting particles/agents arise in multiple disciplines, such as particle systems in physics, flocking birds and migrating cells in biology, and opinion dynamics in social science. An essential task in these applications is to learn the rules of interaction from data. We study the nonparametric regression estimator for the pairwise interaction kernels from trajectory data of differential systems, with examples including opinion dynamics, the Lennard-Jones system, and mean-field PDEs. When the system has finite particles, we have a statistical learning problem; when the system has infinite particles, we have an ill-posed inverse problem for PDEs. Importantly, we provide a systematic learning theory addressing the fundamental issues, such as identifiability and mini-max convergence rate. We also introduce a new regularization method using an adaptive RKHS for the PDE inverse problem. Furthermore, learning kernels in operators emerges as a new topic, and we discuss related open questions.

嘉賓介紹

盧飛任職於約翰霍普金斯大學數學系，副教授。博士畢業於Univeristy of Kansas, 碩士畢業於中科院數學物理研究所，本科畢業於華中科技大學。研究領域包括Applied probability, statistical learning theory, inverse problems, computational model reduction, and data assimilation.