Comparison of the performance and reliability between improved sampling strategies for polynomial chaos expansion

DOI10.3934/mbe.2022351OpenAlexW4284977780MaRDI QIDQ2688361

Konstantin Weise, Thomas R. Knösche, Lucas Poßner, Erik B. Muller

Publication date: 3 March 2023

Published in: Mathematical Biosciences and Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.02192

zbMATH Keywords

optimizationsensitivity analysisuncertainty analysisrandom samplingpolynomial chaosL1-minimization

Mathematics Subject Classification ID

Statistics (62-XX) Probability theory and stochastic processes (60-XX)

Uses Software

• SciPy
• Pygpc

Cites Work

• Unnamed Item
• Exploratory designs for computational experiments
• Selection of polynomial chaos bases via Bayesian model uncertainty methods with applications to sparse approximation of PDEs with stochastic inputs
• Compressive sampling of polynomial chaos expansions: convergence analysis and sampling strategies
• Sparse Legendre expansions via \(\ell_1\)-minimization
• Adaptive sparse polynomial chaos expansion based on least angle regression
• Enhancing \(\ell_1\)-minimization estimates of polynomial chaos expansions using basis selection
• The restricted isometry property and its implications for compressed sensing
• On compressive sensing applied to radar
• On the use of variance reducing multipliers in Monte Carlo computations of a global sensitivity index
• Coherence motivated sampling and convergence analysis of least squares polynomial chaos regression
• Least angle regression. (With discussion)
• Sparse polynomial chaos expansions via compressed sensing and D-optimal design
• Variance-based adaptive sequential sampling for polynomial chaos expansion
• Least squares polynomial chaos expansion: a review of sampling strategies
• A near-optimal sampling strategy for sparse recovery of polynomial chaos expansions
• Atomic Decomposition by Basis Pursuit
• A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code
• Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures
• Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics
• From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
• Spectral Methods for Uncertainty Quantification
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
• Optimized Projections for Compressed Sensing
• On Projection Matrix Optimization for Compressive Sensing Systems
• The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
• Stable signal recovery from incomplete and inaccurate measurements
• Monte Carlo sampling methods using Markov chains and their applications
• The Homogeneous Chaos
• Compressed sensing

This page was built for publication: Comparison of the performance and reliability between improved sampling strategies for polynomial chaos expansion