Nonlinear methods for model reduction

DOI10.1051/m2an/2020057zbMath1476.41004arXiv2005.02565OpenAlexW3049629553MaRDI QIDQ5006316

Albert Cohen, Andrea Bonito, Guergana Petrova, Diane Guignard, Ronald A. DeVore, Peter Jantsch

Publication date: 13 August 2021

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.02565

zbMATH Keywords

parametric PDEspiecewise polynomialsreduced modeling

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Multidimensional problems (41A63) Approximation by polynomials (41A10) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58)

Related Items

Linear/ridge expansions: enhancing linear approximations by ridge functions, Reduced basis methods for time-dependent problems, State Estimation with Model Reduction and Shape Variability. Application to biomedical problems, Reduced order modeling for elliptic problems with high contrast diffusion coefficients, Optimal Reduced Model Algorithms for Data-Based State Estimation, Nonlinear Reduced Models for State and Parameter Estimation

Cites Work

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• Nonlinear Kolmogorov widths
• An adaptive local reduced basis method for solving PDEs with uncertain inputs and evaluating risk
• Greedy algorithms for reduced bases in Banach spaces
• Polynomial approximation of anisotropic analytic functions of several variables
• Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs
• A parameterized-background data-weak approach to variational data assimilation: formulation, analysis, and application to acoustics
• Sparse polynomial approximation of parametric elliptic PDEs. Part I: affine coefficients
• Convergence Rates for Greedy Algorithms in Reduced Basis Methods
• Reduced Basis Greedy Selection Using Random Training Sets
• Multivariate Approximation in Downward Closed Polynomial Spaces
• 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