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.
CITATION STYLE
Proctor, J. L., Brunton, S. L., Brunton, B. W., & Kutz, J. N. (2014, December 13). Exploiting sparsity and equation-free architectures in complex systems. European Physical Journal: Special Topics. Springer Verlag. https://doi.org/10.1140/epjst/e2014-02285-8
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