Reduced-space Gaussian Process Regression for data-driven probabilistic forecast of chaotic dynamical systems
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Sapsis_Reduced-space Gaussian.pdf
Description
Submitted version
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4.94 MB
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Author(s)
Wan, Zhong Yi
Sapsis, Themistoklis Panagiotis
Date Issued
2017
Journal
Physica D: Nonlinear Phenomena
Publisher
Elsevier BV
Citation
Wan, Zhong Yi, and Themistoklis P. Sapsis. "Reduced-Space Gaussian Process Regression for Data-Driven Probabilistic Forecast of Chaotic Dynamical Systems." Physica D-Nonlinear Phenomena 345 (2017): 40-55.
Version
Original manuscript
Abstract
© 2016 Elsevier B.V. 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.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/J.PHYSD.2016.12.005
