Sparse sensing and machine learning strategies for characterizing complex dynamical systems

Jose Nathan Kutz
University of Washington

Sparse sensing is used to determine the flow characteristics around a cylinder (Reynolds number and pressure/flow field) from a sparse number of pressure measurements on the cylinder. Using a supervised machine learning strategy, library elements encoding the dimensionally reduced dynamics are computed for various Reynolds numbers. The use of convex $L^1$ optimization is then used with a limited number of pressure measurements on the cylinder to reconstruct the full pressure field and the resulting flow field around the cylinder. Aside from the highly turbulent regime (large Reynold's number) where only the Reynold's number can be identified, accurate reconstruction of the pressure field, flow field and Reynold's number are achieved. The combination of dimensionality reduction, sparse sensing, and machine learning can be broadly applied to characterizing complex dynamical systems through limited measurements and/or sensors.

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