We present a novel theoretical and computational framework based on tensor algebra and hypergraph representation to study higher order or multiway interactions which naturally arise in many biological, social, and complex engineering systems. The proposed framework exploits hidden correlations/redundancies that may be present in the higher order interactions to enable compact representation and efficient computations, and is amenable to data-driven model learning, analysis, and control. 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. Furthermore, we develop higher-order generalization of balanced proper orthogonal decomposition (BPOD) and its variants for model reduction and identification of MLTI systems from data. We propose another tensor-based system representation to characterize the multiway nonlinear dynamics on hypergraphs and derive a Kalman-rank-like condition to identify the minimum number of driver nodes to achieve hypergraph controllability. We will also discuss notions of hypergraph dissimilarity measures to characterize structural differences between two hypergraphs. Finally, we demonstrate our framework on a variety of biological and engineering simulated and experimental datasets.
Amit Surana is a Technical Fellow at Raytheon Technologies Research Center (formerly known as United Technologies Research Center (UTRC)) where he drives research and development in the areas of dynamics and controls, machine learning and collaborative autonomy, with a broad range of aerospace and defense applications. He has won several awards including Padmakar P. Lele Outstanding Research and Thesis award for his PhD Thesis at MIT, Technical Excellence Award at UTRC, and Grainger Grant from the Grainger Foundation and National Academy of Engineering. He has published 22 journal papers, 50 peer reviewed conference papers, and has 4 patents granted and 8 patents pending. Amit received his Bachelor’s degree in Mechanical Engineering from Indian Institute of Technology Bombay in 2000, his M.S. in Mechanical Engineering and M.A. in Mathematics both from Pennsylvania State University in 2002 and 2003, respectively, and his PhD in Mechanical Engineering from Massachusetts Institute of Technology (MIT) in 2007.
