swMATH ID: 30277
Software Authors: Loiseau, Jean-Christophe; Brunton, Steven L.
Description: 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 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.
Homepage: https://faculty.washington.edu/kutz/page26/
Dependencies: Matlab
Keywords: low-dimensional models; nonlinear dynamical systems
Related Software: redbKIT; Nek5000; PDE-Net; VAMPnets; Adam; Loewner; MUMPS; UNLocBoX; PRMLT; Path2Models; SciPy; ElemStatLearn; SINDy-PI; DeepXDE; DiffSharp; AlexNet; ImageNet; TempoGAN; pix2pix; CycleGAN
Referenced in: 31 Publications

Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
Constrained sparse Galerkin regression. Zbl 1419.76205
Loiseau, Jean-Christophe; Brunton, Steven L.

Referencing Publications by Year