In biological and engineering systems, structure, function and dynamics are highly coupled. Such multiway interactions can be naturally and compactly captured via tensor-based representations. Exploiting recent advances in tensor algebraic methods, we develop novel theoretical and computational approaches for data-driven model learning, analysis and control of such tensor-based representations. In one line of work, we extend classical linear time-invariant (LTI) system notions including stability, reachability and observability to multilinear time-invariant (MLTI) systems, in which the state, inputs and outputs are preserved as tensors, and express these notions in terms of more standard concepts of tensor ranks/decompositions. We also introduce a tensor decomposition-based model reduction framework which can significantly reduce the number of MLTI system parameters. In another line of work, we develop the notion of entropy for uniform hypergraphs, which can capture higher order interactions between entities than classical graphs. We show that this tensor entropy is an extension of von Neumann entropy for graphs and can be used as a measure of regularity for uniform hypergraphs. Moreover, we employ uniform hypergraphs for studying controllability of high-dimensional networked systems. We propose another tensor-based multilinear system representation to characterize the multidimensional state dynamics of uniform hypergraphs, and derive a Kalman-rank-like condition to identify the minimum number of control nodes needed to achieve full control of the whole hypergraph. We demonstrate these new tensor-based theoretical and computational developments in a variety of biological and engineering examples.

Can's advisors are Tony Bloch and Indika Rajapaske.

Zoom - https://umich.zoom.us/j/91237438790
Passcode: 456865 Speaker(s): Can Chen (UM)