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

Hampton, Jerrad; Doostan, Alireza

doi:10.1016/j.jcp.2014.09.019

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

Journal Article · Thu Jan 01 00:00:00 EST 2015 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2014.09.019· OSTI ID:1247014

Hampton, Jerrad; Doostan, Alireza

Not Available

View Accepted Manuscript (Publisher)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: SC0006402

OSTI ID:: 1247014

Alternate ID(s):: OSTI ID: 22382160

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 280; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (27)

Sparse Legendre expansions via ℓ1-minimization Rauhut, Holger; Ward, Rachel Journal of Approximation Theory, Vol. 164, Issue 5 https://doi.org/10.1016/j.jat.2012.01.008	journal	May 2012
Multi-resolution analysis of Wiener-type uncertainty propagation schemes Le Maı̂tre, O. P.; Najm, H. N.; Ghanem, R. G. Journal of Computational Physics, Vol. 197, Issue 2 https://doi.org/10.1016/j.jcp.2003.12.020	journal	July 2004
Adaptive sparse polynomial chaos expansion based on least angle regression Blatman, Géraud; Sudret, Bruno Journal of Computational Physics, Vol. 230, Issue 6 https://doi.org/10.1016/j.jcp.2010.12.021	journal	March 2011
A non-adapted sparse approximation of PDEs with stochastic inputs Doostan, Alireza; Owhadi, Houman Journal of Computational Physics, Vol. 230, Issue 8 https://doi.org/10.1016/j.jcp.2011.01.002	journal	April 2011
Reweighted minimization method for stochastic elliptic differential equations Yang, Xiu; Karniadakis, George Em Journal of Computational Physics, Vol. 248 https://doi.org/10.1016/j.jcp.2013.04.004	journal	September 2013
Selection of polynomial chaos bases via Bayesian model uncertainty methods with applications to sparse approximation of PDEs with stochastic inputs Karagiannis, Georgios; Lin, Guang Journal of Computational Physics, Vol. 259 https://doi.org/10.1016/j.jcp.2013.11.016	journal	February 2014
A weighted -minimization approach for sparse polynomial chaos expansions Peng, Ji; Hampton, Jerrad; Doostan, Alireza Journal of Computational Physics, Vol. 267 https://doi.org/10.1016/j.jcp.2014.02.024	journal	June 2014
“Coarse” stability and bifurcation analysis using stochastic simulators: Kinetic Monte Carlo examples Makeev, Alexei G.; Maroudas, Dimitrios; Kevrekidis, Ioannis G. The Journal of Chemical Physics, Vol. 116, Issue 23 https://doi.org/10.1063/1.1476929	journal	June 2002
Asymptotic analysis of the Hermite polynomials from their differential–difference equation Dominici, Diego Journal of Difference Equations and Applications, Vol. 13, Issue 12 https://doi.org/10.1080/10236190701458824	journal	December 2007
Asymptotic forms for Laguerre polynomials Muckenhoupt, Benjamin Proceedings of the American Mathematical Society, Vol. 24, Issue 2 https://doi.org/10.1090/S0002-9939-1970-0251272-9	journal	February 1970
Monte Carlo sampling methods using Markov chains and their applications Hastings, W. K. Biometrika, Vol. 57, Issue 1 https://doi.org/10.1093/biomet/57.1.97	journal	April 1970
Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information Candes, E.J.; Romberg, J.; Tao, T. IEEE Transactions on Information Theory, Vol. 52, Issue 2, p. 489-509 https://doi.org/10.1109/TIT.2005.862083	journal	February 2006
Compressed sensing Donoho, D. L. IEEE Transactions on Information Theory, Vol. 52, Issue 4 https://doi.org/10.1109/TIT.2006.871582	journal	April 2006
A Probabilistic and RIPless Theory of Compressed Sensing Candes, Emmanuel J.; Plan, Yaniv IEEE Transactions on Information Theory, Vol. 57, Issue 11 https://doi.org/10.1109/TIT.2011.2161794	journal	November 2011
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images Bruckstein, Alfred M.; Donoho, David L.; Elad, Michael SIAM Review, Vol. 51, Issue 1, p. 34-81 https://doi.org/10.1137/060657704	journal	February 2009
Probing the Pareto Frontier for Basis Pursuit Solutions van den Berg, Ewout; Friedlander, Michael P. SIAM Journal on Scientific Computing, Vol. 31, Issue 2 https://doi.org/10.1137/080714488	journal	January 2009
Generalized Jacobi Weights, Christoffel Functions, and Jacobi Polynomials Nevai, Paul; Erdélyi, Tamás; Magnus, Alphonse P. SIAM Journal on Mathematical Analysis, Vol. 25, Issue 2 https://doi.org/10.1137/S0036141092236863	journal	March 1994
Atomic Decomposition by Basis Pursuit Chen, Scott Shaobing; Donoho, David L.; Saunders, Michael A. SIAM Review, Vol. 43, Issue 1 https://doi.org/10.1137/S003614450037906X	journal	January 2001
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations Xiu, Dongbin; Karniadakis, George Em SIAM Journal on Scientific Computing, Vol. 24, Issue 2 https://doi.org/10.1137/S1064827501387826	journal	January 2002
Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure Soize, Christian; Ghanem, Roger SIAM Journal on Scientific Computing, Vol. 26, Issue 2 https://doi.org/10.1137/S1064827503424505	journal	January 2004
Atomic Decomposition by Basis Pursuit Chen, Scott Shaobing; Donoho, David L.; Saunders, Michael A. SIAM Journal on Scientific Computing, Vol. 20, Issue 1, p. 33-61 https://doi.org/10.1137/S1064827596304010	journal	January 1998
A survey of cross-validation procedures for model selection Arlot, Sylvain; Celisse, Alain Statistics Surveys, Vol. 4, Issue 0 https://doi.org/10.1214/09-SS054	journal	January 2010
STOCHASTIC COLLOCATION ALGORITHMS USING l1-MINIMIZATION Yan, Liang; Guo, Ling; Xiu, Dongbin International Journal for Uncertainty Quantification, Vol. 2, Issue 3 https://doi.org/10.1615/Int.J.UncertaintyQuantification.2012003925	journal	January 2012
Dimensionality Reduction for Complex Models via Bayesian Compressive Sensing Sargsyan, Khachik; Safta, Cosmin; Najm, Habib N. International Journal for Uncertainty Quantification, Vol. 4, Issue 1 https://doi.org/10.1615/Int.J.UncertaintyQuantification.2013006821	journal	January 2014
Sparse Multiresolution Regression for Uncertainty Propagation Schiavazzi, Daniele; Doostan, Alireza; Iaccarino, Gianluca International Journal for Uncertainty Quantification, Vol. 4, Issue 4 https://doi.org/10.1615/Int.J.UncertaintyQuantification.2014010147	journal	January 2014
Mean Convergence of Expansions in Laguerre and Hermite Series Askey, Richard; Wainger, Stephen American Journal of Mathematics, Vol. 87, Issue 3 https://doi.org/10.2307/2373069	journal	July 1965
A Compressed Sensing Approach for Partial Differential Equations with Random Input Data Mathelin, L.; Gallivan, K. A. Communications in Computational Physics, Vol. 12, Issue 4 https://doi.org/10.4208/cicp.151110.090911a	journal	October 2012

Similar Records

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

Journal Article · Wed Dec 31 23:00:00 EST 2014 · Journal of Computational Physics · OSTI ID:22382160

Least squares polynomial chaos expansion: A review of sampling strategies

Journal Article · Sat Mar 31 20:00:00 EDT 2018 · Computer Methods in Applied Mechanics and Engineering · OSTI ID:1691673

Least squares polynomial chaos expansion: A review of sampling strategies

Journal Article · Sun Apr 01 00:00:00 EDT 2018 · Computer Methods in Applied Mechanics and Engineering · OSTI ID:1538118

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

Citation Formats

References (27)

Similar Records

Related Subjects