A data-driven method for parametric PDE eigenvalue problems using Gaussian process with different covariance functions

DOI10.1515/cmam-2023-0086zbMath1543.65178MaRDI QIDQ6589774

Abdul Hakim Halim, Fleurianne Bertrand, Moataz Alghamdi, Daniele Boffi

Publication date: 20 August 2024

Published in: Computational Methods in Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

splinescovariance functionmachine learningreduced order modelingGaussian process regressionPDE eigenvalue problems

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Model reduction in optics and electromagnetic theory (78M34)

Cites Work

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• Approximate methods for stochastic eigenvalue problems
• Generalized additive models
• Smoothing noisy data with spline functions: Estimating the correct degree of smoothing by the method of generalized cross-validation
• Reduced order modeling for nonlinear structural analysis using Gaussian process regression
• Data-driven reduced order modeling for time-dependent problems
• The approximation of one matrix by another of lower rank.
• Sparse Tensor Approximation of Parametric Eigenvalue Problems
• A POD reduced-order model for eigenvalue problems with application to reactor physics
• Reduced basis approximation anda posteriorierror estimates for parametrized elliptic eigenvalue problems
• Simultaneous reduced basis approximation of parameterized elliptic eigenvalue problems
• Numerical solution of parametrized Navier–Stokes equations by reduced basis methods
• Output bounds for reduced-basis approximations of symmetric positive definite eigenvalue problems
• Reduced Basis Methods for Partial Differential Equations
• A Correspondence Between Bayesian Estimation on Stochastic Processes and Smoothing by Splines
• Multivariate Gaussian processes: definitions, examples and applications
• Data-driven reduced order modeling for parametric PDE eigenvalue problems using Gaussian process regression

Related Items (2)

Reduced basis approximation of parametric eigenvalue problems in presence of clusters and intersections ⋮ Computational methods in applied mathematics (CMAM 2022 Conference, Part 2)

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