Sparsity and Equation-Free Methods for Complex Systems
Nathan Kutz
Department of Applied Mathematics, University of Washington
Date and time:
Friday, April 11, 2014 - 3:00pm
Location:
ECCR 265
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.