Using automatic differentiation for compressive sensing in uncertainty quantification

DOI10.1080/10556788.2017.1359267zbMath1453.94032OpenAlexW2744147826MaRDI QIDQ4685570

Alex Pothen, Guang Lin, Mu Wang

Publication date: 9 October 2018

Published in: Optimization Methods and Software (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10556788.2017.1359267

zbMATH Keywords

automatic differentiationHermite polynomialsuncertainty quantificationcompressive sensingreverse modegeneralized polynomial chaos expansion

Mathematics Subject Classification ID

Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Probabilistic methods, stochastic differential equations (65C99)

Uses Software

• dcc

Cites Work

• Reweighted \(\ell_1\) minimization method for stochastic elliptic differential equations
• A weighted \(\ell_1\)-minimization approach for sparse polynomial chaos expansions
• A non-adapted sparse approximation of PDEs with stochastic inputs
• A Bayesian mixed shrinkage prior procedure for spatial-stochastic basis selection and evaluation of gPC expansions: applications to elliptic SPDEs
• Enhancing \(\ell_1\)-minimization estimates of polynomial chaos expansions using basis selection
• Enhancing sparsity of Hermite polynomial expansions by iterative rotations
• Enhancing sparsity by reweighted \(\ell _{1}\) minimization
• On polynomial chaos expansion via gradient-enhanced \(\ell_1\)-minimization
• Active Subspaces
• The Art of Differentiating Computer Programs
• Evaluating Derivatives
• From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
• The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
• DIMENSIONALITY REDUCTION FOR COMPLEX MODELS VIA BAYESIAN COMPRESSIVE SENSING
• High-Order Collocation Methods for Differential Equations with Random Inputs
• A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
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