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.

References in zbMATH (referenced in 14 articles , 1 standard article )

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  1. Bengana, Y.; Loiseau, J.-Ch.; Robinet, J.-Ch.; Tuckerman, L. S.: Bifurcation analysis and frequency prediction in shear-driven cavity flow (2019)
  2. Koc, Birgul; Mohebujjaman, Muhammad; Mou, Changhong; Iliescu, Traian: Commutation error in reduced order modeling of fluid flows (2019)
  3. Leclercq, Colin; Demourant, Fabrice; Poussot-Vassal, Charles; Sipp, Denis: Linear iterative method for closed-loop control of quasiperiodic flows (2019)
  4. Mangan, N. M.; Askham, T.; Brunton, S. L.; Kutz, J. N.; Proctor, J. L.: Model selection for hybrid dynamical systems via sparse regression (2019)
  5. Rudy, Samuel; Alla, Alessandro; Brunton, Steven L.; Kutz, J. Nathan: Data-driven identification of parametric partial differential equations (2019)
  6. Fick, Lambert; Maday, Yvon; Patera, Anthony T.; Taddei, Tommaso: A stabilized POD model for turbulent flows over a range of Reynolds numbers: optimal parameter sampling and constrained projection (2018)
  7. Ibáñez, Rubén; Abisset-Chavanne, Emmanuelle; Ammar, Amine; González, David; Cueto, Elías; Huerta, Antonio; Duval, Jean Louis; Chinesta, Francisco: A multidimensional data-driven sparse identification technique: the sparse proper generalized decomposition (2018)
  8. Kaiser, E.; Kutz, J. N.; Brunton, S. L.: Sparse identification of nonlinear dynamics for model predictive control in the low-data limit (2018)
  9. Loiseau, Jean-Christophe; Brunton, Steven L.: Constrained sparse Galerkin regression (2018)
  10. Loiseau, Jean-Christophe; Noack, Bernd R.; Brunton, Steven L.: Sparse reduced-order modelling: sensor-based dynamics to full-state estimation (2018)
  11. Xie, X.; Mohebujjaman, M.; Rebholz, L. G.; Iliescu, T.: Data-driven filtered reduced order modeling of fluid flows (2018)
  12. Zhang, Sheng; Lin, Guang: Robust data-driven discovery of governing physical laws with error bars (2018)
  13. Mangan, N. M.; Kutz, J. N.; Brunton, S. L.; Proctor, J. L.: Model selection for dynamical systems via sparse regression and information criteria (2017)
  14. Mohebujjaman, Muhammad; Rebholz, Leo G.; Xie, Xuping; Iliescu, Traian: Energy balance and mass conservation in reduced-order models of fluid flows (2017)