Sparse polynomial chaos expansions: Literature survey and benchmark

N Lüthen, S Marelli, B Sudret - SIAM/ASA Journal on Uncertainty …, 2021‏ - SIAM
Sparse polynomial chaos expansions (PCE) are a popular surrogate modelling method that
takes advantage of the properties of PCE, the sparsity-of-effects principle, and powerful …

Randomized numerical linear algebra: Foundations and algorithms

PG Martinsson, JA Tropp - Acta Numerica, 2020‏ - cambridge.org
This survey describes probabilistic algorithms for linear algebraic computations, such as
factorizing matrices and solving linear systems. It focuses on techniques that have a proven …

[كتاب][B] An invitation to compressive sensing

S Foucart, H Rauhut, S Foucart, H Rauhut - 2013‏ - Springer
This first chapter formulates the objectives of compressive sensing. It introduces the
standard compressive problem studied throughout the book and reveals its ubiquity in many …

Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm

D Needell, R Ward, N Srebro - Advances in neural …, 2014‏ - proceedings.neurips.cc
We improve a recent gurantee of Bach and Moulines on the linear convergence of SGD for
smooth and strongly convex objectives, reducing a quadratic dependence on the strong …

Compressive sensing and structured random matrices

H Rauhut - Theoretical foundations and numerical methods for …, 2010‏ - degruyter.com
These notes give a mathematical introduction to compressive sensing focusing on recovery
using1-minimization and structured random matrices. An emphasis is put on techniques for …

[كتاب][B] Numerical fourier analysis

G Plonka, D Potts, G Steidl, M Tasche - 2018‏ - Springer
The Applied and Numerical Harmonic Analysis (ANHA) book series aims to provide the
engineering, mathematical, and scientific communities with significant developments in …

A non-adapted sparse approximation of PDEs with stochastic inputs

A Doostan, H Owhadi - Journal of Computational Physics, 2011‏ - Elsevier
We propose a method for the approximation of solutions of PDEs with stochastic coefficients
based on the direct, ie, non-adapted, sampling of solutions. This sampling can be done by …

Extracting sparse high-dimensional dynamics from limited data

H Schaeffer, G Tran, R Ward - SIAM Journal on Applied Mathematics, 2018‏ - SIAM
Extracting governing equations from dynamic data is an essential task in model selection
and parameter estimation. The form of the governing equation is rarely known a priori; …

Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies

J Hampton, A Doostan - Journal of Computational Physics, 2015‏ - Elsevier
Sampling orthogonal polynomial bases via Monte Carlo is of interest for uncertainty
quantification of models with random inputs, using Polynomial Chaos (PC) expansions. It is …

Exact recovery of chaotic systems from highly corrupted data

G Tran, R Ward - Multiscale Modeling & Simulation, 2017‏ - SIAM
Learning the governing equations in dynamical systems from time-varying measurements is
of great interest across different scientific fields. This task becomes prohibitive when such …