Non-intrusive data-driven reduced-order modeling for time-dependent parametrized problems

DOI10.1016/j.jcp.2023.112621arXiv2303.02986OpenAlexW4388486046MaRDI QIDQ6119246

Junming Duan, Jan S. Hesthaven

Publication date: 29 February 2024

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2303.02986

zbMATH Keywords

nonlinear problemreduced-order modelingdynamic mode decompositiontime-dependent problemparametrized problemconvolutional autoencoder

Mathematics Subject Classification ID

Numerical linear algebra (65Fxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx)

Cites Work

• Unnamed Item
• The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows
• A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs
• Non-intrusive reduced order modeling of nonlinear problems using neural networks
• An `empirical interpolation' method: Application to efficient reduced-basis discretization of partial differential equations
• Reduced order modeling for nonlinear structural analysis using Gaussian process regression
• Multi-level convolutional autoencoder networks for parametric prediction of spatio-temporal dynamics
• POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition
• Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders
• Data-driven operator inference for nonintrusive projection-based model reduction
• Über die beste Annäherung von Funktionen einer gegebenen Funktionenklasse
• Parametric dynamic mode decomposition for reduced order modeling
• A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
• Certified Reduced Basis Methods for Parametrized Partial Differential Equations
• Online Adaptive Model Reduction for Nonlinear Systems via Low-Rank Updates
• Adaptiveh-refinement for reduced-order models
• Nonlinear Model Reduction via Discrete Empirical Interpolation
• Dynamic mode decomposition of numerical and experimental data
• 7 Manifold interpolation
• Hyper-reduction of mechanical models involving internal variables
• Missing Point Estimation in Models Described by Proper Orthogonal Decomposition
• Nonlinear model reduction on metric spaces. Application to one-dimensional conservative PDEs in Wasserstein spaces
• Modern Koopman Theory for Dynamical Systems
• Model Reduction for Transport-Dominated Problems via Online Adaptive Bases and Adaptive Sampling
• High-Order Accurate Entropy Stable Finite Difference Schemes for One- and Two-Dimensional Special Relativistic Hydrodynamics
• Higher Order Dynamic Mode Decomposition
• Reduced Basis Methods for Partial Differential Equations
• Reduced basis methods for time-dependent problems
• A data-driven surrogate modeling approach for time-dependent incompressible Navier-Stokes equations with dynamic mode decomposition and manifold interpolation
• Reduced order modeling of parametrized systems through autoencoders and SINDy approach: continuation of periodic solutions