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 (9)

• Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networks
• On closures for reduced order models $-$ A spectrum of first-principle to machine-learned avenues
• Physics-informed Autoencoders for Lyapunov-stable Fluid Flow Prediction
• 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
• Efficient nonlinear manifold reduced order model
• A data driven reduced order model of fluid flow by Auto-Encoder and self-attention deep learning methods

Cited by in corpus (8)

• Operator inference for non-intrusive model reduction with quadratic manifolds
• An AI-based Domain-Decomposition Non-Intrusive Reduced-Order Model for Extended Domains applied to Multiphase Flow in Pipes
• $\text{FastSVD-ML-ROM}$: A Reduced-Order Modeling Framework based on Machine Learning for Real-Time Applications
• Equation-free surrogate modeling of geophysical flows at the intersection of machine learning and data assimilation
• Reduced order modeling for flow and transport problems with Barlow Twins self-supervised learning
• Numerical assessments of a nonintrusive surrogate model based on recurrent neural networks and proper orthogonal decomposition: Rayleigh Benard convection
• Prospects of federated machine learning in fluid dynamics
• Nonintrusive reduced order modeling of convective Boussinesq flows