Applied math seminar which seems to creatively use compressive sensing with machine
learning to characterize dynamics of systems. Could be of interest to some people in the
group who look at compressive sensing, machine learning, dimensionality reduction or
attractors/general chaos theory. Details below:
Location/Time: Lyman 425, 3-4pm
J. Nathan Kutz, University of Washington
Title: Spatiotemporal encoding/decoding of nonlinear dynamics using compressive sensing
and machine learning
Abstract:
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. $L^2$ based dimensionality
reduction methods such as the proper orthogonal decomposition are used for constructing
the machine-learned modal libraries ({\em encoding}) and sparse sensing is used to
identify
and reconstruct the low-dimensional manifolds ({\em decoding}). This technique provides
an objective and general framework for characterizing the underlying dynamics, stability
and bifurcations of complex systems.
The integration of ML and CS techniques also provide an ideal basis for applying control
algorithms to the underlying low-dimensinal dynamical systems. The algorithm works
equally well with experimental data and/or in an equation-free context, for instance by
using dynamic mode decomposition or equation-free modeling in place of POD-type
reductions.
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