Model Reduction of Homogeneous Polynomial Dynamical Systems via Tensor Decomposition

Speaker

Can Chen
Assistant Professor at University of North Carolina at Chapel Hill.

Title

"Model Reduction of Homogeneous Polynomial Dynamical Systems via Tensor Decomposition "

Abstract

Model reduction plays a critical role in system control, with established methods such as balanced truncation widely used for linear systems. However, extending these methods to nonlinear settings, particularly polynomial dynamical systems that are often used to model higher-order interactions in physics, biology, and ecology, remains a significant challenge. In this talk, I will introduce a model reduction method for homogeneous polynomial dynamical systems (HPDSs) with linear input and output grounded in tensor decomposition. Leveraging the inherent tensor structure of HPDSs, we construct reduced models by extracting dominant mode subspaces via higher-order singular value decomposition. Notably, we establish that key system-theoretic properties, including trajectory behavior, controllability, and observability, are preserved in the reduced model. We demonstrate the effectiveness of our method using numerical examples.

About Speaker

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 and a Ph.D. in Applied and Interdisciplinary Mathematics from the University of Michigan in 2020 and 2021, respectively. 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 encompass control theory, network science, machine learning, and bioinformatics.