A deep learning enabler for non-intrusive reduced order modeling of fluid flows

Abstract

In this paper, we introduce a modular deep neural network (DNN) framework for data-driven reduced order modeling of dynamical systems relevant to fluid flows. We propose various deep neural network architectures which numerically predict evolution of dynamical systems by learning from either using discrete state or slope information of the system. Our approach has been demonstrated using both residual formula and backward difference scheme formulas. However, it can be easily generalized into many different numerical schemes as well. We give a demonstration of our framework for three examples: (i) Kraichnan-Orszag system, an illustrative coupled nonlinear ordinary differential equations, (ii) Lorenz system exhibiting chaotic behavior, and (iii) a non-intrusive model order reduction framework for the two-dimensional Boussinesq equations with a differentially heated cavity flow setup at various Rayleigh numbers. Using only snapshots of state variables at discrete time instances, our data-driven approach can be considered truly non-intrusive, since any prior information about the underlying governing equations is not required for generating the reduced order model. Our \textit{a posteriori} analysis shows that the proposed data-driven approach is remarkably accurate, and can be used as a robust predictive tool for non-intrusive model order reduction of complex fluid flows.

arXiv comment36 pages, 21 figures

References in corpus (30)

• Practical Bayesian Optimization of Machine Learning Algorithms
• Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
• Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis
• Sparsity-promoting dynamic mode decomposition
• Neural Ordinary Differential Equations
• Spectral proper orthogonal decomposition
• Stable Architectures for Deep Neural Networks
• Proper Orthogonal Decomposition Closure Models For Turbulent Flows: A Numerical Comparison
• Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks
• Hybrid Forecasting of Chaotic Processes: Using Machine Learning in Conjunction with a Knowledge-Based Model
• Data Driven Governing Equations Approximation Using Deep Neural Networks
• Searching for turbulence models by artificial neural network
• Sparse reduced-order modeling : Sensor-based dynamics to full-state estimation
• Dynamic Mode Decomposition for Large and Streaming Datasets
• On the need for a nonlinear subscale turbulence term in POD models as exemplified for a high Reynolds number flow over an Ahmed body
• An artificial neural network framework for reduced order modeling of transient flows
• Multi-Scale Proper Orthogonal Decomposition of Complex Fluid Flows
• Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations
• Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems
• A Deep Learning based Approach to Reduced Order Modeling for Turbulent Flow Control using LSTM Neural Networks
• Deep learning algorithm for data-driven simulation of noisy dynamical system
• Extreme learning machine for reduced order modeling of turbulent geophysical flows
• POD/DEIM Reduced-Order Strategies for Efficient Four Dimensional Variational Data Assimilation
• Reversible Architectures for Arbitrarily Deep Residual Neural Networks
• DR-RNN: A deep residual recurrent neural network for model reduction
• Proper orthogonal decomposition closure models for fluid flows: Burgers equation
• Continuous Data Assimilation Reduced Order Models of Fluid Flow
• A Multiscale Method for Model Order Reduction in PDE Parameter Estimation
• Locally linear embedding for transient cylinder wakes
• Solving Irregular and Data-enriched Differential Equations using Deep Neural Networks

Cited by in corpus (40)

• Convolutional neural network and long short-term memory based reduced order surrogate for minimal turbulent channel flow
• Deep Neural Networks for Nonlinear Model Order Reduction of Unsteady Flows
• Convolutional neural network based hierarchical autoencoder for nonlinear mode decomposition of fluid field data
• A new prediction method of unsteady wake flow by the hybrid deep neural network
• Data-Driven Deep Learning of Partial Differential Equations in Modal Space
• On closures for reduced order models $-$ A spectrum of first-principle to machine-learned avenues
• Data-driven recovery of hidden physics in reduced order modeling of fluid flows
• Experimental velocity data estimation for imperfect particle images using machine learning
• Reservoir computing model of two-dimensional turbulent convection
• Data-driven peakon and periodic peakon travelling wave solutions of some nonlinear dispersive equations via deep learning
• On generalized residue network for deep learning of unknown dynamical systems
• Memory embedded non-intrusive reduced order modeling of non-ergodic flows
• Parameterized Neural Ordinary Differential Equations: Applications to Computational Physics Problems
• An AI-based Domain-Decomposition Non-Intrusive Reduced-Order Model for Extended Domains applied to Multiphase Flow in Pipes
• Nonlinear proper orthogonal decomposition for convection-dominated flows
• Linear and Nonlinear Dimensionality Reduction from Fluid Mechanics to Machine Learning
• Multiscale Proper Orthogonal Decomposition (mPOD) of TR-PIV data-- a Case Study on Stationary and Transient Cylinder Wake Flows
• A priori analysis on deep learning of subgrid-scale parameterizations for Kraichnan turbulence
• Assessments of epistemic uncertainty using Gaussian stochastic weight averaging for fluid-flow regression
• Non-intrusive model reduction of large-scale, nonlinear dynamical systems using deep learning
• Deep-learning assisted reduced order model for high-dimensional flow prediction from sparse data
• Optimization of Pressure Management Strategies for Geological CO2 Sequestration Using Surrogate Model-based Reinforcement Learning
• Extended Dynamic Mode Decomposition for Inhomogeneous Problems
• Sampling and resolution characteristics in reduced order models of shallow water equations: intrusive vs non-intrusive
• Comparison of neural closure models for discretised PDEs
• Model Order Reduction based on Runge-Kutta Neural Network
• A Multifidelity deep operator network approach to closure for multiscale systems
• Non-intrusive reduced order modeling of poroelasticity of heterogeneous media based on a discontinuous Galerkin approximation
• CD-ROM: Complemented Deep-Reduced Order Model
• A Tailored Convolutional Neural Network for Nonlinear Manifold Learning of Computational Physics Data using Unstructured Spatial Discretizations
• Numerical assessments of a nonintrusive surrogate model based on recurrent neural networks and proper orthogonal decomposition: Rayleigh Benard convection
• Reduced-order Model for Fluid Flows via Neural Ordinary Differential Equations
• Validation and parameterization of a novel physics-constrained neural dynamics model applied to turbulent fluid flow
• Generalization capabilities and robustness of hybrid models grounded in physics compared to purely deep learning models
• Parametric 3D Convolutional Autoencoder for the Prediction of Flow Fields in a Bed Configuration of Hot Particles
• Reduced order modeling of fluid flows: Machine learning, Kolmogorov barrier, closure modeling, and partitioning
• Efficient Adjoint Petrov-Galerkin Reduced Order Models for fluid flows governed by the incompressible Navier-Stokes equations
• Enhancing Dynamical System Modeling through Interpretable Machine Learning Augmentations: A Case Study in Cathodic Electrophoretic Deposition
• Nonintrusive reduced order modeling of convective Boussinesq flows
• Direct data-driven forecast of local turbulent heat flux in Rayleigh-Bénard convection