Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems

Abstract

Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing equations onto a subspace spanned by basis functions obtained from the compression of a dataset of solution snapshots. However, this method is intrusive since the projection requires access to the system operators. Further, some systems may require special treatment of nonlinearities to ensure computational efficiency or additional modeling to preserve stability. In this work we propose a deep learning-based strategy for nonlinear model reduction that is inspired by projection-based model reduction where the idea is to identify some optimal low-dimensional representation and evolve it in time. Our approach constructs a modular model consisting of a deep convolutional autoencoder and a modified LSTM network. The deep convolutional autoencoder returns a low-dimensional representation in terms of coordinates on some expressive nonlinear data-supporting manifold. The dynamics on this manifold are then modeled by the modified LSTM network in a computationally efficient manner. An offline unsupervised training strategy that exploits the model modularity is also developed. We demonstrate our model on three illustrative examples each highlighting the model's performance in prediction tasks for fluid systems with large parameter-variations and its stability in long-term prediction.

References in corpus (2)

• Chaos as an Intermittently Forced Linear System
• A Novel Model Order Reduction Approach for Navier-Stokes Equations at High Reynolds Number

Cited by in corpus (38)

• Data-driven discovery of coordinates and governing equations
• Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders
• Multi-level Convolutional Autoencoder Networks for Parametric Prediction of Spatio-temporal Dynamics
• Probabilistic neural networks for fluid flow surrogate modeling and data recovery
• Graph neural networks for laminar flow prediction around random 2D shapes
• Assessment of unsteady flow predictions using hybrid deep learning based reduced order models
• Data-driven recovery of hidden physics in reduced order modeling of fluid flows
• Deep learning-based reduced order models in cardiac electrophysiology
• An autoencoder-based reduced-order model for eigenvalue problems with application to neutron diffusion
• Long short-term memory embedded nudging schemes for nonlinear data assimilation of geophysical flows
• Model fusion with physics-guided machine learning
• An AI-based Domain-Decomposition Non-Intrusive Reduced-Order Model for Extended Domains applied to Multiphase Flow in Pipes
• Parameterized Neural Ordinary Differential Equations: Applications to Computational Physics Problems
• Nonlinear proper orthogonal decomposition for convection-dominated flows
• Embedding Hard Physical Constraints in Neural Network Coarse-Graining of 3D Turbulence
• An advanced hybrid deep adversarial autoencoder for parameterized nonlinear fluid flow modelling
• Latent-space time evolution of non-intrusive reduced-order models using Gaussian process emulation
• Nonlinear model reduction on metric spaces. Application to one-dimensional conservative PDEs in Wasserstein spaces
• Predicting waves in fluids with deep neural network
• Neural-network learning of SPOD latent dynamics
• Predicting fluid-structure interaction with graph neural networks
• Applying Convolutional Neural Networks to Data on Unstructured Meshes with Space-Filling Curves
• The Intrinsic Dimension of Images and Its Impact on Learning
• Coherent Solutions and Transition to Turbulence in Two-Dimensional Rayleigh-Bénard Convection
• POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition
• Deep-learning-based reduced-order modeling for subsurface flow simulation
• A Tailored Convolutional Neural Network for Nonlinear Manifold Learning of Computational Physics Data using Unstructured Spatial Discretizations
• Validation and parameterization of a novel physics-constrained neural dynamics model applied to turbulent fluid flow
• Promoting global stability in data-driven models of quadratic nonlinear dynamics
• Deep Learning for Efficient Reconstruction of High-Resolution Turbulent DNS Data
• Neural Ordinary Differential Equations for Data-Driven Reduced Order Modeling of Environmental Hydrodynamics
• Conditionally Parameterized, Discretization-Aware Neural Networks for Mesh-Based Modeling of Physical Systems
• Reduced order modeling of fluid flows: Machine learning, Kolmogorov barrier, closure modeling, and partitioning
• Kinematically consistent recurrent neural networks for learning inverse problems in wave propagation
• Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models
• Learning Low-Dimensional Quadratic-Embeddings of High-Fidelity Nonlinear Dynamics using Deep Learning
• Direct data-driven forecast of local turbulent heat flux in Rayleigh-Bénard convection
• Solving time-dependent parametric PDEs by multiclass classification-based reduced order model