Data-Driven Correction Reduced Order Models for the Quasi-Geostrophic Equations: A Numerical Investigation

Abstract

This paper investigates the recently introduced data-driven correction reduced order model (DDC-ROM) in the numerical simulation of the quasi-geostrophic equations. The DDC-ROM uses available data to model the correction term that is generally used to represent the missing information in low-dimensional ROMs. Physical constraints are added to the DDC-ROM to create the constrained data-driven correction reduced order model (CDDC-ROM) in order to further improve its accuracy and stability. Finally, the DDC-ROM is tested on time intervals that are longer than the time interval over which it was trained. The numerical investigation shows that, for low-dimensional ROMs, both the DDC-ROM and CDDC-ROM perform better than the standard Galerkin ROM (G-ROM) and the CDDC-ROM provides the best results.

References in corpus (16)

• On Dynamic Mode Decomposition: Theory and Applications
• Proper Orthogonal Decomposition Closure Models For Turbulent Flows: A Numerical Comparison
• Data-assisted reduced-order modeling of extreme events in complex dynamical systems
• Data-Driven POD-Galerkin Reduced Order Model for Turbulent Flows
• Data-driven non-Markovian closure models
• Time-series learning of latent-space dynamics for reduced-order model closure
• Extreme learning machine for reduced order modeling of turbulent geophysical flows
• A discrete approach to stochastic parametrization and dimensional reduction in nonlinear dynamics
• Approximate deconvolution large eddy simulation of a barotropic ocean circulation model
• Physically-Constrained Data-Driven, Filtered Reduced Order Modeling of Fluid Flows
• A stabilized proper orthogonal decomposition reduced-order model for large scale quasigeostrophic ocean circulation
• On a certified Smagorinsky reduced basis turbulence model
• Model Reduction For Parametrized Optimal Control Problems in Environmental Marine Sciences and Engineering
• Data-adaptive harmonic spectra and multilayer Stuart-Landau models
• Variational approach to closure of nonlinear dynamical systems: Autonomous case
• Streamline derivative projection-based POD-ROM for convection-dominated flows. Part I : Numerical Analysis

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• Data-Driven Closure of Projection-Based Reduced Order Models for Unsteady Compressible Flows
• An Efficient Continuous Data Assimilation Algorithm for the Sabra Shell Model of Turbulence