Data-driven recovery of hidden physics in reduced order modeling of fluid flows

Abstract

In this article, we introduce a modular hybrid analysis and modeling (HAM) approach to account for hidden physics in reduced order modeling (ROM) of parameterized systems relevant to fluid dynamics. The hybrid ROM framework is based on using the first principles to model the known physics in conjunction with utilizing the data-driven machine learning tools to model remaining residual that is hidden in data. This framework employs proper orthogonal decomposition as a compression tool to construct orthonormal bases and Galerkin projection (GP) as a model to built the dynamical core of the system. Our proposed methodology hence compensates structural or epistemic uncertainties in models and utilizes the observed data snapshots to compute true modal coefficients spanned by these bases. The GP model is then corrected at every time step with a data-driven rectification using a long short-term memory (LSTM) neural network architecture to incorporate hidden physics. A Grassmannian manifold approach is also adapted for interpolating basis functions to unseen parametric conditions. The control parameter governing the system's behavior is thus implicitly considered through true modal coefficients as input features to the LSTM network. The effectiveness of the HAM approach is discussed through illustrative examples that are generated synthetically to take hidden physics into account. Our approach thus provides insights addressing a fundamental limitation of the physics-based models when the governing equations are incomplete to represent underlying physical processes.

References in corpus (34)

• Machine Learning for Fluid Mechanics
• Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data
• Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations
• Artificial Neural Networks trained through Deep Reinforcement Learning discover control strategies for active flow control
• PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Network
• Ergodic theory, Dynamic Mode Decomposition and Computation of Spectral Properties of the Koopman operator
• Discovering physical concepts with neural networks
• Enforcing Analytic Constraints in Neural-Networks Emulating Physical Systems
• Spectral proper orthogonal decomposition
• Proper Orthogonal Decomposition Closure Models For Turbulent Flows: A Numerical Comparison
• Nonlinear mode decomposition with convolutional neural networks for fluid dynamics
• De-Biasing the Dynamic Mode Decomposition for Applied Koopman Spectral Analysis
• Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders
• Shallow Neural Networks for Fluid Flow Reconstruction with Limited Sensors
• Sparse reduced-order modeling : Sensor-based dynamics to full-state estimation
• Data-assisted reduced-order modeling of extreme events in complex dynamical systems
• 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
• Physics-Informed Probabilistic Learning of Linear Embeddings of Non-linear Dynamics With Guaranteed Stability
• On the stability of projection-based model order reduction for convection-dominated laminar and turbulent flows
• A non-intrusive reduced order modeling framework for quasi-geostrophic turbulence
• POD/DEIM Reduced-Order Strategies for Efficient Four Dimensional Variational Data Assimilation
• Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems
• Feature engineering and symbolic regression methods for detecting hidden physics from sparse sensors
• Physically-Constrained Data-Driven, Filtered Reduced Order Modeling of Fluid Flows
• Proper orthogonal decomposition closure models for fluid flows: Burgers equation
• Approximate deconvolution large eddy simulation of a stratified two-layer quasigeostrophic ocean model
• Memory embedded non-intrusive reduced order modeling of non-ergodic flows
• Data-Driven Correction Reduced Order Models for the Quasi-Geostrophic Equations: A Numerical Investigation
• Physics-guided Design and Learning of Neural Networks for Predicting Drag Force on Particle Suspensions in Moving Fluids
• A Multiscale Method for Model Order Reduction in PDE Parameter Estimation
• An Efficient Coarse Grid Projection Method for Quasigeostrophic Models of Large-Scale Ocean Circulation
• Using Physics-Informed Super-Resolution Generative Adversarial Networks for Subgrid Modeling in Turbulent Reactive Flows

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• Neural Closure Models for Dynamical Systems
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