Reduced basis methods for time-dependent problems
From MaRDI portal
Publication:5887836
DOI10.1017/S0962492922000058OpenAlexW4281695078MaRDI QIDQ5887836
Cecilia Pagliantini, Gianluigi Rozza, Jan S. Hesthaven
Publication date: 14 April 2023
Published in: Acta Numerica (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1017/s0962492922000058
Related Items
Global energy preserving model reduction for multi-symplectic PDEs, Reduced-order modeling for Ablowitz-Ladik equation, Uncertainty quantification for nonlinear solid mechanics using reduced order models with Gaussian process regression, A two-stage deep learning architecture for model reduction of parametric time-dependent problems, Gradient-Preserving Hyper-Reduction of Nonlinear Dynamical Systems via Discrete Empirical Interpolation, Efficient and accurate nonlinear model reduction via first-order empirical interpolation, Surrogate modeling of time-domain electromagnetic wave propagation via dynamic mode decomposition and radial basis function, The mpEDMD Algorithm for Data-Driven Computations of Measure-Preserving Dynamical Systems, Neural Galerkin schemes with active learning for high-dimensional evolution equations, Non-intrusive data-driven reduced-order modeling for time-dependent parametrized problems, Error estimate of the non-intrusive reduced basis (NIRB) two-grid method with parabolic equations, Error estimates of invariant-preserving difference schemes for the rotation-two-component Camassa-Holm system with small energy, Model order reduction for deforming domain problems in a time‐continuous space‐time setting, Reduced order modeling for parametrized generalized Newtonian fluid flows
Uses Software
Cites Work
- Spectral convergence of multiquadric interpolation
- Reduction and reconstruction for self-similar dynamical systems
- Model reduction methods based on Krylov subspaces
- Evaluation of Proper Orthogonal Decomposition--Based Decomposition Techniques Applied to Parameter-Dependent Nonturbulent Flows
- A reduced-order approach for optimal control of fluids using proper orthogonal decomposition
- A priori estimation of memory effects in reduced-order models of nonlinear systems using the Mori–Zwanzig formalism
- Structure Preserving Model Reduction of Parametric Hamiltonian Systems
- Geometric Subspace Updates with Applications to Online Adaptive Nonlinear Model Reduction
- Transport Reversal for Model Reduction of Hyperbolic Partial Differential Equations
- The Shifted Proper Orthogonal Decomposition: A Mode Decomposition for Multiple Transport Phenomena
- Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment
- Freezing Solutions of Equivariant Evolution Equations
- Korteweg-de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion
- Galerkin Proper Orthogonal Decomposition Methods for a General Equation in Fluid Dynamics
- Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
- Conservative Finite-Difference Methods on General Grids
- Interpolation-Based ${\cal H}_2$-Model Reduction of Bilinear Control Systems
- Non‐intrusive reduced‐order modelling of the Navier–Stokes equations based on RBF interpolation
- Missing Point Estimation in Models Described by Proper Orthogonal Decomposition
- Structure-preserving reduced basis methods for Poisson systems
- Modeling synchronization in globally coupled oscillatory systems using model order reduction
- Nonlinear model reduction on metric spaces. Application to one-dimensional conservative PDEs in Wasserstein spaces
- Structure preserving model order reduction of shallow water equations
- Nonlinear methods for model reduction
- Structure-Preserving Interpolatory Model Reduction for Port-Hamiltonian Differential-Algebraic Systems
- Rank-adaptive structure-preserving model order reduction of Hamiltonian systems
- A Registration Method for Model Order Reduction: Data Compression and Geometry Reduction
- Conservative Model Order Reduction for Fluid Flow
- Non-Intrusive Reduced Order Modeling of Convection Dominated Flows Using Artificial Neural Networks with Application to Rayleigh-Taylor Instability
- A space-time hp-interpolation-based certified reduced basis method for Burgers' equation
- Erratum: Active Subspace Methods in Theory and Practice: Applications to Kriging Surfaces
- An "$hp$" Certified Reduced Basis Method for Parametrized Elliptic Partial Differential Equations
- Gradient-Based Dimension Reduction of Multivariate Vector-Valued Functions
- Model Order Reduction for Problems with Large Convection Effects
- Fundamentals of reduced basis method for problems governed by parametrized PDEs and applications
- Preserving Lagrangian Structure in Nonlinear Model Reduction with Application to Structural Dynamics
- Error Analysis of the Dynamically Orthogonal Approximation of Time Dependent Random PDEs
- Convergence Rates of the POD–Greedy Method
- A posteriorierror bounds for reduced-basis approximations of parametrized parabolic partial differential equations
- Structure Preserving Moment Matching for Port-Hamiltonian Systems: Arnoldi and Lanczos
- Interpolation of Functions with Parameter Dependent Jumps by Transformed Snapshots
- Learning representations by back-propagating errors
- A Geometric Approach to Dynamical Model Order Reduction
- Locally Adaptive Greedy Approximations for Anisotropic Parameter Reduced Basis Spaces
- A training set and multiple bases generation approach for parameterized model reduction based on adaptive grids in parameter space
- Efficient greedy algorithms for high-dimensional parameter spaces with applications to empirical interpolation and reduced basis methods
- Localized Discrete Empirical Interpolation Method
- Reduced basis method for finite volume approximations of parametrized linear evolution equations
- Dynamical Low‐Rank Approximation
- Geometric Numerical Integration
- Reduced Basis Methods for Partial Differential Equations
- On the topology of three-dimensional steady flows of an ideal fluid
- Approximation by superpositions of a sigmoidal function
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Discovering governing equations from data by sparse identification of nonlinear dynamical systems
- t-SNE
- Approximated Lax pairs for the reduced order integration of nonlinear evolution equations
- Nonlinear reduced basis approximation of parameterized evolution equations via the method of freezing
- The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows
- A Laplace transform certified reduced basis method; application to the heat equation and wave equation
- Passivity and structure preserving order reduction of linear port-Hamiltonian systems using Krylov subspaces
- A reduced basis method for electromagnetic scattering by multiple particles in three dimensions
- Supervised principal component analysis: visualization, classification and regression on subspaces and submanifolds
- Gaussian functional regression for output prediction: model assimilation and experimental design
- Reduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers' equation
- Solution manifolds and submanifolds of parametrized equations and their discretization errors
- Recurrent neural network closure of parametric POD-Galerkin reduced-order models based on the Mori-Zwanzig formalism
- Data-driven POD-Galerkin reduced order model for turbulent flows
- Dynamically orthogonal field equations for continuous stochastic dynamical systems
- Goal-oriented, model-constrained optimization for reduction of large-scale systems
- Data-driven combined state and parameter reduction for inverse problems
- Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Application to transport and continuum mechanics.
- From quantum to classical molecular dynamics: Reduced models and numerical analysis.
- Structure preserving model reduction of port-Hamiltonian systems by moment matching at infinity
- Dissipativity preserving balancing for nonlinear systems -- a Hankel operator approach
- Interpolatory projection methods for structure-preserving model reduction
- The solution to a generalized Toda lattice and representation theory
- On making large nonlinear problems small
- An SVD-like matrix decomposition and its applications
- Structure-preserving model reduction for mechanical systems
- Reconstruction equations and the Karhunen-Loève expansion for systems with symmetry
- Radial basis functions for the multivariate interpolation of large scattered data sets
- Non-intrusive reduced order modeling of nonlinear problems using neural networks
- Dynamic data-driven reduced-order models
- Energy preserving model order reduction of the nonlinear Schrödinger equation
- An `empirical interpolation' method: Application to efficient reduced-basis discretization of partial differential equations
- Reduced order modelling for unsteady fluid flow using proper orthogonal decomposition and radial basis functions
- Principal component analysis.
- Bayesian learning for neural networks
- Variants of dynamic mode decomposition: boundary condition, Koopman, and Fourier analyses
- Structure-preserving tangential interpolation for model reduction of port-Hamiltonian systems
- Reduced order modeling for nonlinear structural analysis using Gaussian process regression
- Data-driven reduced order modeling for time-dependent problems
- Structure-preserving model reduction for dynamical systems with a first integral
- Dynamical reduced basis methods for Hamiltonian systems
- POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition
- A theoretical analysis of deep neural networks and parametric PDEs
- Non-linearly stable reduced-order models for incompressible flow with energy-conserving finite volume methods
- A Gaussian process regression approach within a data-driven POD framework for engineering problems in fluid dynamics
- A localized reduced-order modeling approach for PDEs with bifurcating solutions
- Non-intrusive reduced order modeling of unsteady flows using artificial neural networks with application to a combustion problem
- Symplectic dynamical low rank approximation of wave equations with random parameters
- Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders
- Structure-preserving Galerkin POD reduced-order modeling of Hamiltonian systems
- Data-driven operator inference for nonintrusive projection-based model reduction
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Structure-preserving model-reduction of dissipative Hamiltonian systems
- Fast low-rank modifications of the thin singular value decomposition
- Greedy algorithms for reduced bases in Banach spaces
- Certified reduced basis approximation for parametrized partial differential equations and applications
- Conservative model reduction for finite-volume models
- Hamiltonian structure for dispersive and dissipative dynamical systems
- Reduced-order modeling of time-dependent PDEs with multiple parameters in the boundary data
- On theoretical and numerical aspects of symplectic Gram-Schmidt-like algorithms
- Reduced-basis methods for elliptic equations in sub-domains with a posteriori error bounds and adaptivity
- Structure-preserving reduced-order modeling of Korteweg-de Vries equation
- Multiresolution Dynamic Mode Decomposition
- A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
- Structure-Preserving Model Reduction for Nonlinear Port-Hamiltonian Systems
- A prioriconvergence of the Greedy algorithm for the parametrized reduced basis method
- A Posteriori Error Estimation for DEIM Reduced Nonlinear Dynamical Systems
- Certified Reduced Basis Methods for Parametrized Partial Differential Equations
- Online Adaptive Model Reduction for Nonlinear Systems via Low-Rank Updates
- Nonlinear model order reduction based on local reduced-order bases
- Structure-preserving, stability, and accuracy properties of the energy-conserving sampling and weighting method for the hyper reduction of nonlinear finite element dynamic models
- Adaptiveh-refinement for reduced-order models
- Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems
- Nonlinear Model Reduction via Discrete Empirical Interpolation
- Dynamic mode decomposition of numerical and experimental data
- Certified Reduced Basis Methods and Output Bounds for the Harmonic Maxwell's Equations
- Convergence Rates for Greedy Algorithms in Reduced Basis Methods
- Topics in structure-preserving discretization
- Simulating Hamiltonian Dynamics
- Reduction methods for nonlinear steady-state thermal analysis
- Machine Learning for Fluid Mechanics
- On the Error Behavior of the Reduced Basis Technique for Nonlinear Finite Element Approximations
- Finite elements in computational electromagnetism
- Finite element exterior calculus, homological techniques, and applications
- Symplectic Model Reduction of Hamiltonian Systems
- Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations
- Hessian-based model reduction for large-scale systems with initial-condition inputs
- Hyper-reduction of mechanical models involving internal variables
- Improved successive constraint method baseda posteriorierror estimate for reduced basis approximation of 2D Maxwell's problem
- Reduced-order modeling of parameterized PDEs using time-space-parameter principal component analysis
- The Reduced Basis Method for Initial Value Problems
- The Reduced Basis Method for Incompressible Viscous Flow Calculations
- Recent advances in reduction methods for nonlinear problems
- Sliced Inverse Regression for Dimension Reduction