Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders

Abstract

A common strategy for the dimensionality reduction of nonlinear partial differential equations relies on the use of the proper orthogonal decomposition (POD) to identify a reduced subspace and the Galerkin projection for evolving dynamics in this reduced space. However, advection-dominated PDEs are represented poorly by this methodology since the process of truncation discards important interactions between higher-order modes during time evolution. In this study, we demonstrate that an encoding using convolutional autoencoders (CAEs) followed by a reduced-space time evolution by recurrent neural networks overcomes this limitation effectively. We demonstrate that a truncated system of only two latent-space dimensions can reproduce a sharp advecting shock profile for the viscous Burgers equation with very low viscosities, and a six-dimensional latent space can recreate the evolution of the inviscid shallow water equations. Additionally, the proposed framework is extended to a parametric reduced-order model by directly embedding parametric information into the latent space to detect trends in system evolution. Our results show that these advection-dominated systems are more amenable to low-dimensional encoding and time evolution by a CAE and recurrent neural network combination than the POD Galerkin technique.

References in corpus (22)

• Deep learning for universal linear embeddings of nonlinear dynamics
• Searching for Activation Functions
• A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problems
• 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
• A Point-Cloud Deep Learning Framework for Prediction of Fluid Flow Fields on Irregular Geometries
• Multi-level Convolutional Autoencoder Networks for Parametric Prediction of Spatio-temporal Dynamics
• An artificial neural network framework for reduced order modeling of transient flows
• Latent ODEs for Irregularly-Sampled Time Series
• A Deep Learning based Approach to Reduced Order Modeling for Turbulent Flow Control using LSTM Neural Networks
• Nonlinear Model Order Reduction via Lifting Transformations and Proper Orthogonal Decomposition
• Time-series learning of latent-space dynamics for reduced-order model closure
• Extreme learning machine for reduced order modeling of turbulent geophysical flows
• Deep convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems
• Physically-Constrained Data-Driven, Filtered Reduced Order Modeling of Fluid Flows
• 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
• A Localized Reduced-Order Modeling Approach for PDEs with Bifurcating Solutions
• Latent-space time evolution of non-intrusive reduced-order models using Gaussian process emulation
• Neural network representability of fully ionized plasma fluid model closures
• Multiobjective Optimal Control Methods for Fluid Flow Using Reduced Order Modeling

Cited by in corpus (63)

• Convolutional neural network based hierarchical autoencoder for nonlinear mode decomposition of fluid field data
• Transformers for Modeling Physical Systems
• Probabilistic neural networks for fluid flow surrogate modeling and data recovery
• Convolutional neural networks for fluid flow analysis: toward effective metamodeling and low-dimensionalization
• Data-driven discovery of intrinsic dynamics
• Data-driven recovery of hidden physics in reduced order modeling of fluid flows
• Experimental velocity data estimation for imperfect particle images using machine learning
• LaSDI: Parametric Latent Space Dynamics Identification
• A Comparison of Neural Network Architectures for Data-Driven Reduced-Order Modeling
• Reduced order modeling of parametrized systems through autoencoders and SINDy approach: continuation of periodic solutions
• Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamics
• Latent Space Data Assimilation by using Deep Learning
• A long short-term memory embedding for hybrid uplifted reduced order models
• Long short-term memory embedded nudging schemes for nonlinear data assimilation of geophysical flows
• Model fusion with physics-guided machine learning
• 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
• Combining physics-based and data-driven models: advancing the frontiers of research with Scientific Machine Learning
• Assessments of epistemic uncertainty using Gaussian stochastic weight averaging for fluid-flow regression
• Non-intrusive data-driven reduced-order modeling for time-dependent parametrized problems
• Towards physically consistent data-driven weather forecasting: Integrating data assimilation with equivariance-preserving deep spatial transformers
• $\text{FastSVD-ML-ROM}$: A Reduced-Order Modeling Framework based on Machine Learning for Real-Time Applications
• Physics-aware Reduced-order Modeling of Transonic Flow via $\beta$-Variational Autoencoder
• Predicting waves in fluids with deep neural network
• Multi-fidelity physics constrained neural networks for dynamical systems
• Neural-network learning of SPOD latent dynamics
• An enhanced parametric nonlinear reduced order model for imperfect structures using Neumann expansion
• Data-Driven Surrogates of Rotating Detonation Engine Physics with Neural ODEs and High-Speed Camera Footage
• GRIDS-Net: Inverse shape design and identification of scatterers via geometric regularization and physics-embedded deep learning
• Robust training approach of neural networks for fluid flow state estimations
• Bi-fidelity Variational Auto-encoder for Uncertainty Quantification
• Reduced-order modeling of unsteady fluid flow using neural network ensembles
• Multi-scale Time-stepping of Partial Differential Equations with Transformers
• CD-ROM: Complemented Deep-Reduced Order Model
• Dynamical system prediction from sparse observations using deep neural networks with Voronoi tessellation and physics constraint
• Generalizability of reservoir computing for flux-driven two-dimensional convection
• Reconstructing three-dimensional bluff body wake from sectional flow fields with convolutional neural networks
• Data Assimilation Predictive GAN (DA-PredGAN): applied to determine the spread of COVID-19
• Neural Ordinary Differential Equations for Model Order Reduction of Stiff Systems
• An experimental modal testing method for subcritical flow around a cylinder
• A Tailored Convolutional Neural Network for Nonlinear Manifold Learning of Computational Physics Data using Unstructured Spatial Discretizations
• Accelerating the convergence of Newton's method for nonlinear elliptic PDEs using Fourier neural operators
• Deep Learning for Reduced Order Modelling and Efficient Temporal Evolution of Fluid Simulations
• CGKN: A Deep Learning Framework for Modeling Complex Dynamical Systems and Efficient Data Assimilation
• Numerical assessments of a nonintrusive surrogate model based on recurrent neural networks and proper orthogonal decomposition: Rayleigh Benard convection
• Real-time forecasting of chaotic dynamics from sparse data and autoencoders
• Conditionally Parameterized, Discretization-Aware Neural Networks for Mesh-Based Modeling of Physical Systems
• Fast PDE-constrained optimization via self-supervised operator learning
• Reduced order modeling of fluid flows: Machine learning, Kolmogorov barrier, closure modeling, and partitioning
• Improving Long-term Autoregressive Spatiotemporal Predictions: A Proof of Concept with Fluid Dynamics
• A composable autoencoder-based iterative algorithm for accelerating numerical simulations
• Polytopic Autoencoders with Smooth Clustering for Reduced-order Modelling of Flows
• Model order reduction with neural networks: Application to laminar and turbulent flows
• A FOM/ROM Hybrid Approach for Accelerating Numerical Simulations
• Data-Augmented Predictive Deep Neural Network: Enhancing the extrapolation capabilities of non-intrusive surrogate models
• Hamiltonian reduction using a convolutional auto-encoder coupled to an Hamiltonian neural network
• A Latent space solver for PDE generalization
• Time-inversion of spatiotemporal beam dynamics using uncertainty-aware latent evolution reversal
• Interpretable and flexible non-intrusive reduced-order models using reproducing kernel Hilbert spaces
• Surrogate models for Rock-Fluid Interaction: A Grid-Size-Invariant Approach
• Decomposition of flow data via gradient-based transport optimization
• Projection-based model-order reduction via graph autoencoders suited for unstructured meshes