Karhunen-Loève expansion revisited for vector-valued random fields: scaling, errors and optimal basis.
From MaRDI portal
Publication:401581
DOI10.1016/j.jcp.2013.02.036zbMath1329.60142OpenAlexW1984478718MaRDI QIDQ401581
C. Funfschilling, Guillaume Perrin, Denis Duhamel, Christian Soize
Publication date: 27 August 2014
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jcp.2013.02.036
Related Items
A biorthogonal decomposition for the identification and simulation of non-stationary and non-Gaussian random fields ⋮ Best estimation of functional linear models ⋮ Monte Carlo algorithm for vector-valued Gaussian functions with preset component accuracies ⋮ Adaptive method for indirect identification of the statistical properties of random fields in a Bayesian framework ⋮ Spectral representation of stochastic field data using sparse polynomial chaos expansions ⋮ Polynomial-chaos-based conditional statistics for probabilistic learning with heterogeneous data applied to atomic collisions of helium on graphite substrate ⋮ Measurements-based constrained control optimization in presence of uncertainties with application to the driver commands for high-speed trains ⋮ Compressed Principal Component Analysis of Non-Gaussian Vectors ⋮ Data-driven probability concentration and sampling on manifold ⋮ Regularized kernel PCA for the efficient parameterization of complex geological models ⋮ Stochastic Galerkin framework with locally reduced bases for nonlinear two-phase transport in heterogeneous formations ⋮ Finite dimensional models for random functions
Cites Work
- A priori reduction method for solving the two-dimensional Burgers' equations
- Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations
- Identification of Bayesian posteriors for coefficients of chaos expansions
- Generalized spectral decomposition for stochastic nonlinear problems
- Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems
- Polynomial chaos representation of spatio-temporal random fields from experimental measurements
- An efficient, high-order perturbation approach for flow in random porous media via Karhunen-Loève and polynomial expansions.
- A Karhunen-Loève least-squares technique for optimization of geometry of a blunt body in supersonic flow.
- Finite elements for stochastic media problems
- Karhunen-Loève approximation of random fields by generalized fast multipole methods
- Convergence study of the truncated Karhunen–Loeve expansion for simulation of stochastic processes
- Generalized probabilistic approach of uncertainties in computational dynamics using random matrices and polynomial chaos decompositions
- Spectral Methods for Uncertainty Quantification
- Numerical tools for analysis and solution of Fredholm integral equations of the first kind
- Evaluation of Proper Orthogonal Decomposition--Based Decomposition Techniques Applied to Parameter-Dependent Nonturbulent Flows
- Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure
- Identification of Polynomial Chaos Representations in High Dimension from a Set of Realizations
- Proper orthogonal decomposition for reduced basis feedback controllers for parabolic equations
- Galerkin proper orthogonal decomposition methods for parabolic problems
