Spatiotemporal encoding/decoding of nonlinear dynamics using compressive sensing and machine learning

J. Nathan Kutz

Department of Applied Mathematics  

University of Washington

Many high-dimensional complex systems often exhibit dynamics that evolve on a slow-manifold and/or a low-dimensional attractor. Thus we propose a data-driven modeling strategy that encodes/decodes the dynamical evolution using compressive (sparse) sensing (CS) in conjunction with machine learning (ML) strategies. The integration of ML and CS techniques also provide an ideal basis for applying control algorithms to the underlying low-dimensinal dynamical systems. The method developed will be applied to neuro-sensory systems which encode their functionality into persistent spatio-temporal patterns of neuron activity, or so-called neural codes. Networks of neurons in the antennal lobe (AL) of moths form such low-dimensional neural codes that compete dynamically with each other through lateral inhibition, thus producing a robust signal-processing unit that increases signal-to-noise and enhances the contrast between neural codes. Moreover, such encoding is conjectured to occur in strain sensors in their wings, thus revealing a method of how robust flight control can be accomplished.