2020/01/01 by Zhuangkun Wei, Bin Li, Chengyao Sun +1 · 7 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Fluorescence Microscopy Techniques #Computer science #Mathematical analysis #Mathematical optimization #Mathematics #Model Reduction and Neural Networks #Neural Networks and Reservoir Computing #Nonlinear system #Observable #Operator (biology) #Physics #Polynomial #Sampling (signal processing) #cs.IT #eess.SP #math.IT
paper · pdf · doi:10.1109/tsp.2020.3032408
published in IEEE Transactions on Signal Processing 68, 6187-6197 (Institute of Electrical and Electronics Engineers)
openalex publication_date 2020/01/01 · openalex created_date 2020/05/01 · arxiv created 2020/10/16 · arxiv updated 2020/12/02 · openalex updated_date 2026/08/05
Monitoring the networked dynamics via the subset of nodes is essential for a variety of scientific and operational purposes. When there is a lack of an explicit model and networked signal space, traditional observability analysis and non-convex methods are insufficient. Current data-driven Koopman linearization, although derives a linear evolution model for selected vector-valued observable of original state-space, may result in a large sampling set due to: (i) the large size of polynomial based observables (O(N2), N number of nodes in network), and (ii) not factoring in the nonlinear dependency between observables. In this work, to achieve linear scaling (O(N)) and a small set of sampling nodes, we propose to combine a novel Log-Koopman operator and nonlinear Graph Fourier Transform (NL-GFT) scheme. First, the Log-Koopman operator is able to reduce the size of observables by transforming multiplicative poly-observable to logarithm summation. Second, a nonlinear GFT concept and sampling theory are provided to exploit the nonlinear dependence of observables for observability analysis using Koopman evolution model. The results demonstrate that the proposed Log-Koopman NL-GFT scheme can (i) linearize unknown nonlinear dynamics using O(N) observables, and (ii) achieve lower number of sampling nodes, compared with the state-of-the art polynomial Koopman based observability analysis.