Nonlinear Reduced Models for State and Parameter Estimation
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Publication:5862904
DOI10.1137/20M1380818zbMath1482.65170arXiv2009.02687OpenAlexW3083124187MaRDI QIDQ5862904
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Publication date: 10 March 2022
Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2009.02687
Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32)
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Cites Work
- Unnamed Item
- Breaking spaces and forms for the DPG method and applications including Maxwell equations
- Concentration inequalities and model selection. Ecole d'Eté de Probabilités de Saint-Flour XXXIII -- 2003.
- Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Application to transport and continuum mechanics.
- Nonlinear Kolmogorov widths
- The generalized empirical interpolation method: stability theory on Hilbert spaces with an application to the Stokes equation
- Global a priori convergence theory for reduced-basis approximations of single-parameter symmetric coercive elliptic partial differential equations
- Greedy algorithms for reduced bases in Banach spaces
- Unsteady flow sensing and estimation via the gappy proper orthogonal decomposition
- Convergence analysis of the Generalized Empirical Interpolation Method
- Adaptivity and variational stabilization for convection-diffusion equations
- A Generalized Empirical Interpolation Method: Application of Reduced Basis Techniques to Data Assimilation
- Beyond Consistent Reconstructions: Optimality and Sharp Bounds for Generalized Sampling, and Application to the Uniform Resampling Problem
- Inverse problems: A Bayesian perspective
- Nonlinear model order reduction based on local reduced-order bases
- A parameterized-background data-weak approach to variational data assimilation: formulation, analysis, and application to acoustics
- Adaptiveh-refinement for reduced-order models
- ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF PARAMETRIC AND STOCHASTIC ELLIPTIC PDE'S
- Convergence Rates for Greedy Algorithms in Reduced Basis Methods
- Reduced Basis Greedy Selection Using Random Training Sets
- Optimal Reduced Model Algorithms for Data-Based State Estimation
- Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization
- Greedy Algorithms for Optimal Measurements Selection in State Estimation Using Reduced Models
- Adaptive Petrov--Galerkin Methods for First Order Transport Equations
- Stability of Galerkin discretizations of a mixed space–time variational formulation of parabolic evolution equations
- Nonlinear methods for model reduction
- A Petrov-Galerkin discretization with optimal test space of a mild-weak formulation of convection-diffusion equations in mixed form
- An "$hp$" Certified Reduced Basis Method for Parametrized Elliptic Partial Differential Equations
- Approximation of high-dimensional parametric PDEs
- Data Assimilation in Reduced Modeling
- Locally Adaptive Greedy Approximations for Anisotropic Parameter Reduced Basis Spaces
- Localized Discrete Empirical Interpolation Method
- Double greedy algorithms: Reduced basis methods for transport dominated problems
- Diffusion Coefficients Estimation for Elliptic Partial Differential Equations
- A RESULT IN HILBERT SPACE
