Stability of Discrete Empirical Interpolation and Gappy Proper Orthogonal Decomposition with Randomized and Deterministic Sampling Points

DOI10.1137/19M1307391zbMath1453.65287arXiv1808.10473OpenAlexW3089316803MaRDI QIDQ5131990

Benjamin Peherstorfer, Serkan Gugercin, Zlatko Drmač

Publication date: 9 November 2020

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.10473

zbMATH Keywords

model reductionnoisy observationsnonlinear model reductionempirical interpolationgappy proper orthogonal decompositionrandomized model reduction

Mathematics Subject Classification ID

Numerical interpolation (65D05) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Orthogonalization in numerical linear algebra (65F25) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)

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Cites Work

• Unnamed Item
• On the stability and accuracy of least squares approximations
• The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows
• Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points
• Sensor placement in nuclear reactors based on the generalized empirical interpolation method
• Stabilization of (G)EIM in presence of measurement noise: application to nuclear reactor physics
• An `empirical interpolation' method: Application to efficient reduced-basis discretization of partial differential equations
• The generalized empirical interpolation method: stability theory on Hilbert spaces with an application to the Stokes equation
• POD-DEIM model order reduction for strain-softening viscoplasticity
• Unsteady flow sensing and estimation via the gappy proper orthogonal decomposition
• Exact matrix completion via convex optimization
• A New Selection Operator for the Discrete Empirical Interpolation Method---Improved A Priori Error Bound and Extensions
• A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
• An Accelerated Greedy Missing Point Estimation Procedure
• A Generalized Empirical Interpolation Method: Application of Reduced Basis Techniques to Data Assimilation
• Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations
• Parameter multi-domain ‘hp ’ empirical interpolation
• Online Adaptive Model Reduction for Nonlinear Systems via Low-Rank Updates
• Nonlinear Model Reduction via Discrete Empirical Interpolation
• The Discrete Empirical Interpolation Method: Canonical Structure and Formulation in Weighted Inner Product Spaces
• Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations
• Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization
• Geometric Subspace Updates with Applications to Online Adaptive Nonlinear Model Reduction
• Greedy Algorithms for Optimal Measurements Selection in State Estimation Using Reduced Models
• Missing Point Estimation in Models Described by Proper Orthogonal Decomposition
• Refined Perturbation Bounds for Eigenvalues of Hermitian and Non-Hermitian Matrices
• Simple models of turbulent flows
• Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs
• Localized Discrete Empirical Interpolation Method