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.