报告题目：Machine Learning and Dynamical Systems meet in Reproducing Kernel Hilbert Spaces

报告所属学科：管理科学与工程

报告人：Boumediene Hamzi（加州理工学院）

报告时间：2024年9月18日 10:00-12:00

报告地点：经管学院702室

报告摘要：

The theory of dynamical systems, developed by Poincare and Lyapunov in the 19th century, studies the qualitative behaviour of systems through models, often involving differential equations. These models can be complex to develop for challenging systems like climate, brain, biological, and financial dynamics. In contrast, machine learning focuses on algorithms that improve with more data, applicable in areas like computer vision, stock market analysis, and social media sentiment analysis. Machine learning excels in scenarios where explicit models are absent but data is available. This talk explores how reproducing kernel Hilbert spaces can bridge dynamical systems theory and machine learning. We introduce methods for learning surrogate models, including parametric and nonparametric kernel flows for chaotic systems, and techniques like Sparse Kernel Flows and Hausdorff-metric based Kernel Flows. We also present a data-based approach for estimating key quantities in nonlinear systems, leveraging kernel methods to approximate controllability and observability energies, model reduction, invariant measures, and Lyapunov functions.

报告人简介：

Boumediene Hamzi is currently a Senior Scientist at the Department of Computing and Mathematical Sciences, Caltech, an Affiliate Fellow of the Data Science Institute at Imperial College London, and a visiting professor at Johns Hopkins University. He is also co-leading the Research Interest Group on Machine Learning and Dynamical Systems at the Alan Turing Institute (London, UK). He has been honoured twice as a Marie Curie Fellow and published more than 100 papers in academic journals including Automatica, SIAM Journal on Control and Optimization, etc. Broadly speaking, his research is at the interface of Machine Learning and Dynamical Systems.