Can Chen: Homogeneous Polynomial Systems Theory through Tensor Decomposition

Abstract: Numerous complex real-world systems, such as those in biological, ecological, and social networks, exhibit higher-order interactions that are often modeled using polynomial dynamical systems or homogeneous polynomial dynamical systems (HPDSs). However, analyzing key system-theoretic properties remains challenging due to their inherent nonlinearity and complexity, particularly for large-scale systems. In this talk, I will introduce an innovative computational framework that leverages advanced tensor decomposition techniques to drive new insights and enable efficient computation in the analysis of HPDSs that can be equivalently represented by tensors. Specifically, I will discuss the use of tensor eigenvalues to assess the stability of HPDSs and derive efficient necessary and sufficient conditions for controllability and observability using tensor decomposition-based representations of HPDSs. The effectiveness and efficiency of the framework are validated through numerical examples.

Bio: Can Chen is an Assistant Professor in the School of Data Science and Society, with secondary appointments in the Department of Mathematics and the Department of Biostatistics at the University of North Carolina at Chapel Hill. He earned his B.S. in Mathematics from the University of California, Irvine in 2016, followed by an M.S. in Electrical and Computer Engineering (2020) and a Ph.D. in Applied and Interdisciplinary Mathematics (2021) from the University of Michigan. From 2021 to 2023, he was a Postdoctoral Research Fellow in the Channing Division of Network Medicine at Brigham and Women’s Hospital and Harvard Medical School. His research interests span a broad range of topics, including control theory, network science, tensor algebra, numerical analysis, data science, machine learning, deep learning, hypergraph learning, data analysis, and computational biology.