Journal
PHYSICA D-NONLINEAR PHENOMENA
Volume 345, Issue -, Pages 40-55Publisher
ELSEVIER
DOI: 10.1016/j.physd.2016.12.005
Keywords
Data-driven prediction; Uncertainty quantification; Order-reduction; Gaussian Process Regression; T21 barotropic climate model; Lorenz 96
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Funding
- National Science Foundation [NSF EAGER ECCS 15-1462254]
- Air Force Office of Scientific Research [AFOSR YIP 16RT0548]
- Office of Naval Research [ONR YIP N00014-15-1-2381]
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We formulate a reduced-order strategy for efficiently forecasting complex high-dimensional dynamical systems entirely based on data streams. The first step of our method involves reconstructing the dynamics in a reduced-order subspace of choice using Gaussian Process Regression (GPR). GPR simultaneously allows for reconstruction of the vector field and more importantly, estimation of local uncertainty. The latter is due to (i) local interpolation error and (ii) truncation of the high-dimensional phase space. This uncertainty component can be analytically quantified in terms of the GPR hyperparameters. In the second step we formulate stochastic models that explicitly take into account the reconstructed dynamics and their uncertainty. For regions of the attractor which are not sufficiently sampled for our GPR framework to be effective, an adaptive blended scheme is formulated to enforce correct statistical steady state properties, matching those of the real data. We examine the effectiveness of the proposed method to complex systems including the Lorenz 96, the Kuramoto-Sivashinsky, as well as a prototype climate model. We also study the performance of the proposed approach as the intrinsic dimensionality of the system attractor increases in highly turbulent regimes. (C) 2016 Elsevier B.V. All rights reserved.
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