On the role of nonlinear correlations in reduced-order modelling
Article dans une revue avec comité de lecture
Date
2022-03Journal
Journal of Fluid MechanicsRésumé
This work investigates nonlinear dimensionality reduction as a means of improving the accuracy and stability of reduced-order models of advection-dominated flows. Nonlinear correlations between temporal proper orthogonal decomposition (POD) coefficients can be exploited to identify latent low-dimensional structure, approximating the attractor with a minimal set of driving modes and a manifold equation for the remaining modes. By viewing these nonlinear correlations as an invariant manifold reduction, this least-order representation can be used to stabilize POD–Galerkin models or as a state space for data-driven model identification. In the latter case, we use sparse polynomial regression to learn a compact, interpretable dynamical system model from the time series of the active modal coefficients. We demonstrate this perspective on a quasiperiodic shear-driven cavity flow and show that the dynamics evolves on a torus generated by two independent Stuart–Landau oscillators. The specific approach to nonlinear correlations analysis used in this work is applicable to periodic and quasiperiodic flows, and cannot be applied to chaotic or turbulent flows. However, the results illustrate the limitations of linear modal representations of advection-dominated flows and motivate the use of nonlinear dimensionality reduction more broadly for exploiting underlying structure in reduced-order models.
Fichier(s) constituant cette publication
- Nom:
- DYNFLUID_JFM_2022_LOISEAU.pdf
- Taille:
- 1.889Mo
- Format:
- Description:
- On the role of nonlinear corre ...
- Fin d'embargo:
- 2022-10-09
Cette publication figure dans le(s) laboratoire(s) suivant(s)
Documents liés
Visualiser des documents liés par titre, auteur, créateur et sujet.
-
Article dans une revue avec comité de lectureImproved turbulence modeling remains a major open problem in mathematical physics. Turbulence is notoriously challenging, in part due to its multiscale nature and the fact that large-scale coherent structures cannot be ...
-
Article dans une revue avec comité de lectureKAPTANOGLU, Alan; DE SILVA, Brian; FASEL, Urban; KAHEMAN, Kadierdan; GOLDSCHMIDT, Andy; CALLAHAM, Jared; DELAHUNT, Charles; NICOLAOU, Zachary; CHAMPION, Kathleen; KUTZ, J.; BRUNTON, Steven; LOISEAU, Jean-Christophe (The Open Journal, 2022-01)Automated data-driven modeling, the process of directly discovering the governing equations of a system from data, is increasingly being used across the scientific community. PySINDy is a Python package that provides tools ...
-
Article dans une revue avec comité de lectureCALLAHAM, J. L.; RIGAS, G.; BRUNTON, S. L.; LOISEAU, Jean-Christophe (The Royal Society Publishing, 2021-06)Many physical systems characterized by nonlinear multiscale interactions can be modelled by treating unresolved degrees of freedom as random fluctuations. However, even when the microscopic governing equations and qualitative ...
-
Article dans une revue avec comité de lectureThe 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 ...
-
Article dans une revue avec comité de lectureDE SILVA, Brian; CHAMPION, Kathleen; QUADE, Markus; KUTZ, J. Nathan; BRUNTON, Steven; LOISEAU, Jean-Christophe (Open Journals, 2020)Scientists have long quantified empirical observations by developing mathematical models that characterize the observations, have some measure of interpretability, and are capable of making predictions. Dynamical systems ...