Nonlinear proper orthogonal decomposition for convection-dominated flows

Abstract

Autoencoder techniques find increasingly common use in reduced order modeling as a means to create a latent space. This reduced order representation offers a modular data-driven modeling approach for nonlinear dynamical systems when integrated with a time series predictive model. In this letter, we put forth a nonlinear proper orthogonal decomposition (POD) framework, which is an end-to-end Galerkin-free model combining autoencoders with long short-term memory networks for dynamics. By eliminating the projection error due to the truncation of Galerkin models, a key enabler of the proposed nonintrusive approach is the kinematic construction of a nonlinear mapping between the full-rank expansion of the POD coefficients and the latent space where the dynamics evolve. We test our framework for model reduction of a convection-dominated system, which is generally challenging for reduced order models. Our approach not only improves the accuracy, but also significantly reduces the computational cost of training and testing.

References in corpus (32)

• Data-driven discovery of coordinates and governing equations
• PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domain
• Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networks
• Neural Ordinary Differential Equations
• Nonlinear mode decomposition with convolutional neural networks for fluid dynamics
• Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders
• Convolutional neural network based hierarchical autoencoder for nonlinear mode decomposition of fluid field data
• A deep learning enabler for non-intrusive reduced order modeling of fluid flows
• Multi-level Convolutional Autoencoder Networks for Parametric Prediction of Spatio-temporal Dynamics
• Physics-Informed Probabilistic Learning of Linear Embeddings of Non-linear Dynamics With Guaranteed Stability
• On closures for reduced order models $-$ A spectrum of first-principle to machine-learned avenues
• Convolutional neural networks for fluid flow analysis: toward effective metamodeling and low-dimensionalization
• Sparse identification of nonlinear dynamics with low-dimensionalized flow representations
• Deep learning to discover and predict dynamics on an inertial manifold
• A non-intrusive reduced order modeling framework for quasi-geostrophic turbulence
• Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems
• An autoencoder-based reduced-order model for eigenvalue problems with application to neutron diffusion
• Recovering missing CFD data for high-order discretizations using deep neural networks and dynamics learning
• Physics-informed Autoencoders for Lyapunov-stable Fluid Flow Prediction
• A long short-term memory embedding for hybrid uplifted reduced order models
• Compressed Convolutional LSTM: An Efficient Deep Learning framework to Model High Fidelity 3D Turbulence
• Model fusion with physics-guided machine learning
• Embedding Hard Physical Constraints in Neural Network Coarse-Graining of 3D Turbulence
• A priori analysis on deep learning of subgrid-scale parameterizations for Kraichnan turbulence
• Latent-space time evolution of non-intrusive reduced-order models using Gaussian process emulation
• Efficient nonlinear manifold reduced order model
• Multifidelity Computing for Coupling Full and Reduced Order Models
• Physics-aware registration based auto-encoder for convection dominated PDEs
• A data driven reduced order model of fluid flow by Auto-Encoder and self-attention deep learning methods
• Lagrangian Data-Driven Reduced Order Modeling of Finite Time Lyapunov Exponents
• Learning a Reduced Basis of Dynamical Systems using an Autoencoder
• Quantum System Compression: A Hamiltonian Guided Walk Through Hilbert Space

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