Sampling and resolution characteristics in reduced order models of shallow water equations: intrusive vs non-intrusive

Abstract

We investigate the sensitivity of reduced order models (ROMs) to training data resolution as well as sampling rate. In particular, we consider proper orthogonal decomposition (POD), coupled with Galerkin projection (POD-GP), as an intrusive reduced order modeling technique. For non-intrusive ROMs, we consider two frameworks. The first is using dynamic mode decomposition (DMD), and the second is based on artificial neural networks (ANNs). For ANN, we utilized a residual deep neural network, and for DMD we have studied two versions of DMD approaches; one with hard thresholding and the other with sorted bases selection. Also, we highlight the differences between mean-subtracting the data (i.e., centering) and using the data without mean-subtraction. We tested these ROMs using a system of 2D shallow water equations for four different numerical experiments, adopting combinations of sampling rates and resolutions. For these cases, we found that the DMD basis obtained with hard threshodling is sensitive to sampling rate, performing worse at very high rates. The sorted DMD algorithm helps to mitigate this problem and yields more stabilized and converging solution. Furthermore, we demonstrate that both DMD approaches with mean subtraction provide significantly more accurate results than DMD with mean-subtracting the data. On the other hand, POD is relatively insensitive to sampling rate and yields better representation of the flow field. Meanwhile, resolution has little effect on both POD and DMD performances. Therefore, we preferred to train the neural network in POD space, since it is more stable and better represents our dataset. Numerical results reveal that an artificial neural network on POD subspace (POD-ANN) performs remarkably better than POD-GP and DMD in capturing system dynamics, even with a small number of modes.

References in corpus (25)

• On Dynamic Mode Decomposition: Theory and Applications
• Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis
• Sparsity-promoting dynamic mode decomposition
• Super-resolution reconstruction of turbulent flows with machine learning
• Spectral proper orthogonal decomposition
• Stable Architectures for Deep Neural Networks
• Proper Orthogonal Decomposition Closure Models For Turbulent Flows: A Numerical Comparison
• De-Biasing the Dynamic Mode Decomposition for Applied Koopman Spectral Analysis
• Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition
• Deep Fluids: A Generative Network for Parameterized Fluid Simulations
• Dynamic Mode Decomposition for Large and Streaming Datasets
• Sparse reduced-order modeling : Sensor-based dynamics to full-state estimation
• Data-Driven POD-Galerkin Reduced Order Model for Turbulent Flows
• On the need for a nonlinear subscale turbulence term in POD models as exemplified for a high Reynolds number flow over an Ahmed body
• A deep learning enabler for non-intrusive reduced order modeling of fluid flows
• An artificial neural network framework for reduced order modeling of transient flows
• Multi-Scale Proper Orthogonal Decomposition of Complex Fluid Flows
• POD/DEIM Nonlinear model order reduction of an ADI implicit shallow water equations model
• Evaluating Data Assimilation Algorithms
• pyMOR - Generic Algorithms and Interfaces for Model Order Reduction
• Physically-Constrained Data-Driven, Filtered Reduced Order Modeling of Fluid Flows
• Proper orthogonal decomposition closure models for fluid flows: Burgers equation
• Dynamic mode decomposition for multiscale nonlinear physics
• Reduced-order modeling for cardiac electrophysiology. Application to parameter identification
• POD/DEIM Reduced-Order Modeling of Time-Fractional Partial Differential Equations with Applications in Parameter Identification

Cited by in corpus (7)

• An AI-based Domain-Decomposition Non-Intrusive Reduced-Order Model for Extended Domains applied to Multiphase Flow in Pipes
• Assessments of epistemic uncertainty using Gaussian stochastic weight averaging for fluid-flow regression
• Parallel Reduced Order Modeling for Digital Twins using High-Performance Computing Workflows
• High-Fidelity Digital Twin Data Models by Randomized Dynamic Mode Decomposition and Deep Learning with Applications in Fluid Dynamics
• Energy preserving reduced-order modelling of thermal shallow water equation
• Sketching Methods for Dynamic Mode Decomposition in Spherical Shallow Water Equations
• Well-balanced POD-based reduced-order models for finite volume approximation of hyperbolic balance laws