期刊
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
卷 223, 期 13, 页码 2665-2684出版社
SPRINGER HEIDELBERG
DOI: 10.1140/epjst/e2014-02285-8
关键词
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Complex systems exhibit dynamics that typically evolve on low-dimensional attractors and may have sparse representation in some optimal basis. Recently developed compressive sensing techniques exploit this sparsity for state reconstruction and/or categorical identification from limited measurements. We argue that data-driven dimensionality reduction methods integrate naturally with sparse sensing in the context of complex systems. This framework works equally well with a physical model or in an equation-free context, where data is available but the governing equations may be unknown. We demonstrate the advantages of combining these methods on three prototypical examples: classification of dynamical regimes, optimal sensor placement, and equation-free dynamic model reduction. These examples motivate the potentially transformative role that state-of-the-art data methods and machine learning can play in the analysis of complex systems.
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