Constrained sparse Galerkin regression

The sparse identification of nonlinear dynamics (SINDy) is a recently proposed data-driven modelling framework that uses sparse regression techniques to identify nonlinear low-order models. With the goal of low-order models of a fluid flow, we combine this approach with dimensionality reduction tech...

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Vydáno v:Journal of fluid mechanics Ročník 838; s. 42 - 67
Hlavní autoři: Loiseau, Jean-Christophe, Brunton, Steven L.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cambridge, UK Cambridge University Press 10.03.2018
Cambridge University Press (CUP)
Témata:
Algorithms
Artificial intelligence
Cavity flow
Circular cylinders
Computational fluid dynamics
Constraint modelling
Cylinders
Dynamical systems
Dynamics
Engineering Sciences
Fluid Dynamics
Fluid flow
Fluids mechanics
Frameworks
Galerkin method
Identification
JFM Papers
Mathematical models
Mechanics
Model accuracy
Modelling
Navier-Stokes equations
Nonlinear dynamics
Nonlinear systems
Partial differential equations
Physics
Proper Orthogonal Decomposition
Reduced order models
Regression analysis
Regression models
Two dimensional flow
nonlinear dynamical systems
low-dimensional models
ISSN:0022-1120, 1469-7645
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Shrnutí:The sparse identification of nonlinear dynamics (SINDy) is a recently proposed data-driven modelling framework that uses sparse regression techniques to identify nonlinear low-order models. With the goal of low-order models of a fluid flow, we combine this approach with dimensionality reduction techniques (e.g. proper orthogonal decomposition) and extend it to enforce physical constraints in the regression, e.g. energy-preserving quadratic nonlinearities. The resulting models, hereafter referred to as Galerkin regression models, incorporate many beneficial aspects of Galerkin projection, but without the need for a high-fidelity solver to project the Navier–Stokes equations. Instead, the most parsimonious nonlinear model is determined that is consistent with observed measurement data and satisfies necessary constraints. Galerkin regression models also readily generalize to include higher-order nonlinear terms that model the effect of truncated modes. The effectiveness of such an approach is demonstrated on two canonical flow configurations: the two-dimensional flow past a circular cylinder and the shear-driven cavity flow. For both cases, the accuracy of the identified models compare favourably against reduced-order models obtained from a standard Galerkin projection procedure. Finally, the entire code base for our constrained sparse Galerkin regression algorithm is freely available online.
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ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2017.823