2015/06/01 by Ido Bright, Guang Lin, Bright, Ido +3
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Artificial intelligence #Asynchronous communication #Compressed sensing #Computer science #Computer vision #Digital Holography and Microscopy #Dynamical Systems (math.DS) #FOS: Mathematics #Gaussian #Leverage (statistics) #Matching pursuit #Model Reduction and Neural Networks #Neural Networks and Reservoir Computing #Physics #Sampling (signal processing) #Snapshot (computer storage) #Spacetime #Sparse approximation #Sparse matrix #math.DS
paper · pdf · doi:10.48550/arxiv.1506.00661
19 pages, 4 figures
arxiv created 2015/06/01 · openalex publication_date 2015/06/01 · arxiv updated 2015/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a novel method for the classification and reconstruction of time dependent, high-dimensional data using sparse measurements, and apply it to the flow around a cylinder. Assuming the data lies near a low dimensional manifold (low-rank dynamics) in space and has periodic time dependency with a sparse number of Fourier modes, we employ compressive sensing for accurately classifying the dynamical regime. We further show that we can reconstruct the full spatio-temporal behavior with these limited measurements, extending previous results of compressive sensing that apply for only a single snapshot of data. The method can be used for building improved reduced-order models and designing sampling/measurement strategies that leverage time asynchrony.