Data-driven reduced order modeling for parametric PDE eigenvalue problems using Gaussian process regression
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Publication:6087951
DOI10.1016/j.jcp.2023.112503arXiv2301.08934MaRDI QIDQ6087951
Abdul Hakim Halim, Fleurianne Bertrand, Daniele Boffi
Publication date: 16 November 2023
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2301.08934
eigenvalue problemproper orthogonal decompositionreduced basis methodGaussian process regressionnon-intrusive method
Spectral theory and eigenvalue problems for partial differential equations (35Pxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx)
Cites Work
- Unnamed Item
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- Fast non-overlapping Schwarz domain decomposition methods for solving the neutron diffusion equation
- Adaptive finite element methods for computing band gaps in photonic crystals
- Principal eigenvalue minimization for an elliptic problem with indefinite weight and Robin boundary conditions
- A reduced-order method for simulation and control of fluid flows
- Reduced order modeling for nonlinear structural analysis using Gaussian process regression
- Data-driven reduced order modeling for time-dependent problems
- A stabilized finite element method for the two-field and three-field Stokes eigenvalue problems
- Analysis of quasi-Monte Carlo methods for elliptic eigenvalue problems with stochastic coefficients
- A posteriori error estimation for planar linear elasticity by stress reconstruction
- Eigenvalue analysis for acoustic problem in 3D by boundary element method with the block Sakurai-Sugiura method
- A successive constraint linear optimization method for lower bounds of parametric coercivity and inf-sup stability constants
- Dimension reduction of large-scale systems. Proceedings of a workshop, Oberwolfach, Germany, October 19--25, 2003.
- A reduced order model for the finite element approximation of eigenvalue problems
- Finite element approximation of eigenvalue problems
- Certified Reduced Basis Methods for Parametrized Partial Differential Equations
- Introduction to Uncertainty Quantification
- 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
- The Reduced Basis Method for Incompressible Viscous Flow Calculations
- A Mathematical and Computational Framework for Reliable Real-Time Solution of Parametrized Partial Differential Equations
- Output bounds for reduced-basis approximations of symmetric positive definite eigenvalue problems
- Adaptive Finite Element Method for the Maxwell Eigenvalue Problem
- Arnold--Winther Mixed Finite Elements for Stokes Eigenvalue Problems
- On the problem of spurious eigenvalues in the approximation of linear elliptic problems in mixed form
- Galerkin Proper Orthogonal Decomposition Methods for a General Equation in Fluid Dynamics
- Optimal Localization of Eigenfunctions in an Inhomogeneous Medium
- Mixed Finite Element Methods and Applications
- Coupled FE–BE method for eigenvalue analysis of elastic structures submerged in an infinite fluid domain
- Advanced Lectures on Machine Learning
- Reduced Basis Methods for Partial Differential Equations
- Level set methods for optimization problems involving geometry and constraints. I: Frequencies of a two-density inhomogeneous drum
- Galerkin proper orthogonal decomposition methods for parabolic problems
