Low-dimensional and computationally less-expensive reduced-order models (ROMs) have been widely used to capture the dominant behaviors of high-4dimensional systems. An ROM can be obtained, using the well-known proper orthogonal decomposition (POD), by projecting the full-order model to a subspace spanned by modal basis modes that are learned from experimental, simulated, or observational data, i.e., training data. However, the optimal basis can change with the parameter settings. When an ROM, constructed using the POD basis obtained from training data, is applied to new parameter settings, the model often lacks robustness against the change of parameters in design, control, and other real-time operation problems. This paper proposes to use regression trees on Grassmann manifold to learn the mapping between parameters and POD bases that span the low-dimensional subspaces onto which full-order models are projected. Motivated by the observation that a subspace spanned by a POD basis can be viewed as a point in the Grassmann manifold, we propose to grow a tree by repeatedly splitting the tree node to maximize the Riemannian distance between the two subspaces spanned by the predicted POD bases on the left and right daughter nodes. Five numerical examples are presented to comprehensively demonstrate the performance of the proposed method, and compare the proposed tree-based method to the existing interpolation method for POD basis and the use of global POD basis. The results show that the proposed tree-based method is capable of establishing the mapping between parameters and POD bases, and thus adapt ROMs for new parameters.
Reduced-Order Quasilinear Model of Ocean Boundary-Layer Turbulence
The combined effectiveness of model reduction and the quasilinear approximation for the reproduction of the low-order statistics of oceanic surface boundary layer turbulence is investigated. Idealized horizontally homogeneous problems of surface-forced thermal convection and Langmuir turbulence are studied in detail. Model reduction is achieved with a Galerkin projection of the governing equations onto a subset of modes determined by proper orthogonal decomposition (POD). When applied to boundary layers that are horizontally homogeneous, POD and a horizontally averaged quasilinear approximation both assume flow features that are horizontally wavelike, making the pairing very efficient. For less than 0.2% of the modes retained, the reduced quasilinear model is able to reproduce vertical profiles of horizontal mean fields as well as certain energetically important second-order turbulent transport statistics and energies to within 30% error. Reduced-basis quasilinear statistics must approach the full-basis statistics as the basis size approaches completion; however, some quasilinear statistics resemble those found in the fully nonlinear simulations at smaller basis truncations. Thus, model reduction could possibly improve upon the accuracy of quasilinear dynamics.
more » « less- PAR ID:
- 10135672
- Publisher / Repository:
- American Meteorological Society
- Date Published:
- Journal Name:
- Journal of Physical Oceanography
- Volume:
- 50
- Issue:
- 3
- ISSN:
- 0022-3670
- Page Range / eLocation ID:
- p. 537-558
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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