메뉴 건너뛰기




Volumn 267, Issue , 2014, Pages 92-111

A weighted ℓ1-minimization approach for sparse polynomial chaos expansions

Author keywords

Basis pursuit denoising (BPDN); Compressive sampling; Polynomial chaos; Sparse approximation; Stochastic PDEs; Uncertainty quantification

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; NUMERICAL METHODS; POLYNOMIAL APPROXIMATION; STOCHASTIC SYSTEMS;

EID: 84896322105     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2014.02.024     Document Type: Article
Times cited : (206)

References (69)
  • 1
    • 0037159819 scopus 로고    scopus 로고
    • Mid-frequency structural dynamics with parameter uncertainty
    • Ghanem R., Sarkar A. Mid-frequency structural dynamics with parameter uncertainty. Comput. Methods Appl. Mech. Eng. 2002, 191:5499-5513.
    • (2002) Comput. Methods Appl. Mech. Eng. , vol.191 , pp. 5499-5513
    • Ghanem, R.1    Sarkar, A.2
  • 2
    • 0037249229 scopus 로고    scopus 로고
    • The Wiener-Askey polynomial chaos for stochastic differential equations
    • Xiu D., Karniadakis G. The Wiener-Askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput. 2002, 24(2):619-644.
    • (2002) SIAM J. Sci. Comput. , vol.24 , Issue.2 , pp. 619-644
    • Xiu, D.1    Karniadakis, G.2
  • 3
    • 0037299084 scopus 로고    scopus 로고
    • Uncertainty quantification in reacting-flow simulations through non-intrusive spectral projection
    • Reagan M., Najm H., Ghanem R., Knio O. Uncertainty quantification in reacting-flow simulations through non-intrusive spectral projection. Combust. Flame 2003, 132(3):545-555.
    • (2003) Combust. Flame , vol.132 , Issue.3 , pp. 545-555
    • Reagan, M.1    Najm, H.2    Ghanem, R.3    Knio, O.4
  • 5
    • 33646577797 scopus 로고    scopus 로고
    • High-order collocation methods for differential equations with random inputs
    • Xiu D., Hesthaven J. High-order collocation methods for differential equations with random inputs. SIAM J. Sci. Comput. 2005, 27(3):1118-1139.
    • (2005) SIAM J. Sci. Comput. , vol.27 , Issue.3 , pp. 1118-1139
    • Xiu, D.1    Hesthaven, J.2
  • 6
    • 34548216854 scopus 로고    scopus 로고
    • A stochastic collocation method for elliptic partial differential equations with random input data
    • Babuška I., Nobile F., Tempone R. A stochastic collocation method for elliptic partial differential equations with random input data. SIAM J. Numer. Anal. 2007, 45(3):1005-1034.
    • (2007) SIAM J. Numer. Anal. , vol.45 , Issue.3 , pp. 1005-1034
    • Babuška, I.1    Nobile, F.2    Tempone, R.3
  • 12
    • 67349208768 scopus 로고    scopus 로고
    • A least-squares approximation of partial differential equations with high-dimensional random inputs
    • Doostan A., Iaccarino G. A least-squares approximation of partial differential equations with high-dimensional random inputs. J. Comput. Phys. 2009, 228(12):4332-4345.
    • (2009) J. Comput. Phys. , vol.228 , Issue.12 , pp. 4332-4345
    • Doostan, A.1    Iaccarino, G.2
  • 13
    • 84878994105 scopus 로고    scopus 로고
    • Non-intrusive low-rank separated approximation of high-dimensional stochastic models
    • Doostan A., Validi A., Iaccarino G. Non-intrusive low-rank separated approximation of high-dimensional stochastic models. Comput. Methods Appl. Mech. Eng. 2013, 263(1):42-55.
    • (2013) Comput. Methods Appl. Mech. Eng. , vol.263 , Issue.1 , pp. 42-55
    • Doostan, A.1    Validi, A.2    Iaccarino, G.3
  • 15
    • 77549083181 scopus 로고    scopus 로고
    • An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis
    • Blatman G., Sudret B. An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis. Probab. Eng. Mech. 2010, 25(2):183-197.
    • (2010) Probab. Eng. Mech. , vol.25 , Issue.2 , pp. 183-197
    • Blatman, G.1    Sudret, B.2
  • 16
    • 79951768991 scopus 로고    scopus 로고
    • A non-adapted sparse approximation of PDEs with stochastic inputs
    • Doostan A., Owhadi H. A non-adapted sparse approximation of PDEs with stochastic inputs. J. Comput. Phys. 2011, 230:3015-3034.
    • (2011) J. Comput. Phys. , vol.230 , pp. 3015-3034
    • Doostan, A.1    Owhadi, H.2
  • 17
    • 78751706487 scopus 로고    scopus 로고
    • Adaptive sparse polynomial chaos expansion based on least angle regression
    • Blatman G., Sudret B. Adaptive sparse polynomial chaos expansion based on least angle regression. J. Comput. Phys. 2011, 230:2345-2367.
    • (2011) J. Comput. Phys. , vol.230 , pp. 2345-2367
    • Blatman, G.1    Sudret, B.2
  • 18
    • 84860662510 scopus 로고    scopus 로고
    • A compressed sensing approach for partial differential equations with random input data
    • Mathelin L., Gallivan K. A compressed sensing approach for partial differential equations with random input data. Commun. Comput. Phys. 2012, 12:919-954.
    • (2012) Commun. Comput. Phys. , vol.12 , pp. 919-954
    • Mathelin, L.1    Gallivan, K.2
  • 20
    • 84877881686 scopus 로고    scopus 로고
    • ℓ1 minimization method for stochastic elliptic differential equations
    • ℓ1 minimization method for stochastic elliptic differential equations. J. Comput. Phys. 2013, 248:87-108.
    • (2013) J. Comput. Phys. , vol.248 , pp. 87-108
    • Yang, X.1    Karniadakis, G.E.2
  • 22
    • 0035273106 scopus 로고    scopus 로고
    • Atomic decomposition by basis pursuit
    • Chen S., Donoho D., Saunders M. Atomic decomposition by basis pursuit. SIAM Rev. 2001, 43(1):129-159.
    • (2001) SIAM Rev. , vol.43 , Issue.1 , pp. 129-159
    • Chen, S.1    Donoho, D.2    Saunders, M.3
  • 23
    • 33645712892 scopus 로고    scopus 로고
    • Compressed sensing
    • Donoho D. Compressed sensing. IEEE Trans. Inf. Theory 2006, 52(4):1289-1306.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.4 , pp. 1289-1306
    • Donoho, D.1
  • 24
    • 31744440684 scopus 로고    scopus 로고
    • Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
    • Candès E., Romberg J., Tao T. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inf. Theory 2006, 52(2):489-509.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.2 , pp. 489-509
    • Candès, E.1    Romberg, J.2    Tao, T.3
  • 25
    • 33744726904 scopus 로고    scopus 로고
    • Quantitative robust uncertainty principles and optimally sparse decompositions
    • Candès E., Romberg J. Quantitative robust uncertainty principles and optimally sparse decompositions. Found. Comput. Math. 2006, 6(2):227-254.
    • (2006) Found. Comput. Math. , vol.6 , Issue.2 , pp. 227-254
    • Candès, E.1    Romberg, J.2
  • 26
    • 33947416035 scopus 로고    scopus 로고
    • Near optimal signal recovery from random projections: Universal encoding strategies?
    • Candès E., Tao T. Near optimal signal recovery from random projections: Universal encoding strategies?. IEEE Trans. Inf. Theory 2006, 52(12):5406-5425.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.12 , pp. 5406-5425
    • Candès, E.1    Tao, T.2
  • 27
    • 34249687049 scopus 로고    scopus 로고
    • Sparsity and incoherence in compressive sampling
    • Candès E., Romberg J. Sparsity and incoherence in compressive sampling. Inverse Probl. 2007, 23(3):969-985.
    • (2007) Inverse Probl. , vol.23 , Issue.3 , pp. 969-985
    • Candès, E.1    Romberg, J.2
  • 28
    • 85032750937 scopus 로고    scopus 로고
    • An introduction to compressive sampling
    • Candès E., Wakin M. An introduction to compressive sampling. IEEE Signal Process. Mag. 2008, 25(2):21-30.
    • (2008) IEEE Signal Process. Mag. , vol.25 , Issue.2 , pp. 21-30
    • Candès, E.1    Wakin, M.2
  • 29
    • 59749104367 scopus 로고    scopus 로고
    • From sparse solutions of systems of equations to sparse modeling of signals and images
    • Bruckstein A., Donoho D., Elad M. From sparse solutions of systems of equations to sparse modeling of signals and images. SIAM Rev. 2009, 51(1):34-81.
    • (2009) SIAM Rev. , vol.51 , Issue.1 , pp. 34-81
    • Bruckstein, A.1    Donoho, D.2    Elad, M.3
  • 30
    • 0034215549 scopus 로고    scopus 로고
    • A new approach to variable selection in least squares problems
    • Osborne M.R., Presnell B., Turlach B.A. A new approach to variable selection in least squares problems. IMA J. Numer. Anal. 2000, 20(3):389-403.
    • (2000) IMA J. Numer. Anal. , vol.20 , Issue.3 , pp. 389-403
    • Osborne, M.R.1    Presnell, B.2    Turlach, B.A.3
  • 31
    • 7044231546 scopus 로고    scopus 로고
    • An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
    • Daubechies I., Defrise M., Mol C.D. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun. Pure Appl. Math. 2004, 57(11):1413-1457.
    • (2004) Commun. Pure Appl. Math. , vol.57 , Issue.11 , pp. 1413-1457
    • Daubechies, I.1    Defrise, M.2    Mol, C.D.3
  • 32
    • 30844438177 scopus 로고    scopus 로고
    • Signal recovery by proximal forward-backward splitting
    • Combettes P.L., Wajs V.R. Signal recovery by proximal forward-backward splitting. Multiscale Model. Simul. 2005, 4(4):1168-1200.
    • (2005) Multiscale Model. Simul. , vol.4 , Issue.4 , pp. 1168-1200
    • Combettes, P.L.1    Wajs, V.R.2
  • 33
    • 39449126969 scopus 로고    scopus 로고
    • Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems
    • Figueiredo M., Nowak R.D., Wright S.J. Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems. IEEE J. Sel. Top. Signal Process. 2007, 1(4):586-597.
    • (2007) IEEE J. Sel. Top. Signal Process. , vol.1 , Issue.4 , pp. 586-597
    • Figueiredo, M.1    Nowak, R.D.2    Wright, S.J.3
  • 36
    • 73149095169 scopus 로고    scopus 로고
    • Message-passing algorithms for compressed sensing
    • Donoho D., Maleki A., Montanari A. Message-passing algorithms for compressed sensing. Proc. Natl. Acad. Sci. USA 2009, 106(45):18914-18919.
    • (2009) Proc. Natl. Acad. Sci. USA , vol.106 , Issue.45 , pp. 18914-18919
    • Donoho, D.1    Maleki, A.2    Montanari, A.3
  • 37
    • 13844319204 scopus 로고    scopus 로고
    • Galerkin finite element approximations of stochastic elliptic partial differential equations
    • Babuška I., Tempone R., Zouraris G. Galerkin finite element approximations of stochastic elliptic partial differential equations. SIAM J. Numer. Anal. 2004, 42(2):800-825.
    • (2004) SIAM J. Numer. Anal. , vol.42 , Issue.2 , pp. 800-825
    • Babuška, I.1    Tempone, R.2    Zouraris, G.3
  • 38
    • 77957936449 scopus 로고    scopus 로고
    • Convergence rates of best n-term Galerkin approximations for a class of elliptic sPDEs
    • Cohen A., DeVore R., Schwab C. Convergence rates of best n-term Galerkin approximations for a class of elliptic sPDEs. Found. Comput. Math. 2010, 10(6):615-646.
    • (2010) Found. Comput. Math. , vol.10 , Issue.6 , pp. 615-646
    • Cohen, A.1    DeVore, R.2    Schwab, C.3
  • 39
    • 84864348351 scopus 로고    scopus 로고
    • On the optimal polynomial approximation of stochastic PDEs by Galerkin and collocation methods
    • Beck J., Nobile F., Tamellini L., Tempone R. On the optimal polynomial approximation of stochastic PDEs by Galerkin and collocation methods. Math. Models Methods Appl. Sci. 2012, 22(09):1250023.
    • (2012) Math. Models Methods Appl. Sci. , vol.22 , Issue.9 , pp. 1250023
    • Beck, J.1    Nobile, F.2    Tamellini, L.3    Tempone, R.4
  • 40
    • 33947134817 scopus 로고    scopus 로고
    • On the use of a priori information for sparse signal approximations
    • Escoda O., Granai L., Vandergheynst P. On the use of a priori information for sparse signal approximations. IEEE Trans. Signal Process. 2006, 9:3468-3482.
    • (2006) IEEE Trans. Signal Process. , vol.9 , pp. 3468-3482
    • Escoda, O.1    Granai, L.2    Vandergheynst, P.3
  • 44
    • 29144439194 scopus 로고    scopus 로고
    • Decoding by linear programming
    • Candès E., Tao T. Decoding by linear programming. IEEE Trans. Inf. Theory 2005, 51(12):4203-4215.
    • (2005) IEEE Trans. Inf. Theory , vol.51 , Issue.12 , pp. 4203-4215
    • Candès, E.1    Tao, T.2
  • 45
    • 33745604236 scopus 로고    scopus 로고
    • Stable signal recovery from incomplete and inaccurate measurements
    • Candès E., Romberg J., Tao T. Stable signal recovery from incomplete and inaccurate measurements. Commun. Pure Appl. Math. 2006, LIX:1207-1223.
    • (2006) Commun. Pure Appl. Math. , vol.49 , pp. 1207-1223
    • Candès, E.1    Romberg, J.2    Tao, T.3
  • 51
    • 84878468242 scopus 로고    scopus 로고
    • Analytic regularity and nonlinear approximation of a class of parametric semilinear elliptic PDEs
    • Hansen M., Schwab C. Analytic regularity and nonlinear approximation of a class of parametric semilinear elliptic PDEs. Math. Nachr. 2013, 286(8-9):832-860. 10.1002/mana.201100131.
    • (2013) Math. Nachr. , vol.286 , Issue.8-9 , pp. 832-860
    • Hansen, M.1    Schwab, C.2
  • 52
    • 84891302382 scopus 로고    scopus 로고
    • Sparse tensor Galerkin discretization of parametric and random parabolic PDEs-analytic regularity and generalized polynomial chaos approximation
    • Hoang V.H., Schwab C. Sparse tensor Galerkin discretization of parametric and random parabolic PDEs-analytic regularity and generalized polynomial chaos approximation. SIAM J. Math. Anal. 2013, 45(5):3050-3083.
    • (2013) SIAM J. Math. Anal. , vol.45 , Issue.5 , pp. 3050-3083
    • Hoang, V.H.1    Schwab, C.2
  • 53
    • 84884858222 scopus 로고    scopus 로고
    • Analytic regularity and GPC approximation for control problems constrained by linear parametric elliptic and parabolic PDEs
    • Kunoth A., Schwab C. Analytic regularity and GPC approximation for control problems constrained by linear parametric elliptic and parabolic PDEs. SIAM J. Control Optim. 2013, 51(3):2442-2471.
    • (2013) SIAM J. Control Optim. , vol.51 , Issue.3 , pp. 2442-2471
    • Kunoth, A.1    Schwab, C.2
  • 54
    • 65649137930 scopus 로고    scopus 로고
    • Probing the Pareto frontier for basis pursuit solutions
    • van den Berg E., Friedlander M.P. Probing the Pareto frontier for basis pursuit solutions. SIAM J. Sci. Comput. 2008, 31(2):890-912.
    • (2008) SIAM J. Sci. Comput. , vol.31 , Issue.2 , pp. 890-912
    • van den Berg, E.1    Friedlander, M.P.2
  • 57
    • 0347968052 scopus 로고    scopus 로고
    • Sparse representations in unions of bases
    • Gribonval R., Nielsen M. Sparse representations in unions of bases. IEEE Trans. Inf. Theory 2003, 49(12):3320-3325.
    • (2003) IEEE Trans. Inf. Theory , vol.49 , Issue.12 , pp. 3320-3325
    • Gribonval, R.1    Nielsen, M.2
  • 58
    • 57349181932 scopus 로고    scopus 로고
    • Compressed sensing and best k-term approximation
    • Cohen A., Dahmen W., DeVore R. Compressed sensing and best k-term approximation. J. Am. Math. Soc. 2009, 22:211-231.
    • (2009) J. Am. Math. Soc. , vol.22 , pp. 211-231
    • Cohen, A.1    Dahmen, W.2    DeVore, R.3
  • 61
    • 42649140570 scopus 로고    scopus 로고
    • The restricted isometry property and its implications for compressed sensing
    • Candès E.J. The restricted isometry property and its implications for compressed sensing. C. R. Math. 2008, 346(9):589-592.
    • (2008) C. R. Math. , vol.346 , Issue.9 , pp. 589-592
    • Candès, E.J.1
  • 62
    • 78651562982 scopus 로고    scopus 로고
    • Tech. Rep. Research Report No. 2009-07, Seminar für Angewandte Mathematik, SAM, Zürich, Switzerland
    • Bieri M., Andreev R., Schwab C. Sparse tensor discretization of elliptic sPDEs 2009, Tech. Rep. Research Report No. 2009-07, Seminar für Angewandte Mathematik, SAM, Zürich, Switzerland.
    • (2009) Sparse tensor discretization of elliptic sPDEs
    • Bieri, M.1    Andreev, R.2    Schwab, C.3
  • 64
    • 0001224048 scopus 로고    scopus 로고
    • Sparse Bayesian learning and the relevance vector machine
    • Tipping M.E. Sparse Bayesian learning and the relevance vector machine. J. Mach. Learn. Res. 2001, 1:211-244.
    • (2001) J. Mach. Learn. Res. , vol.1 , pp. 211-244
    • Tipping, M.E.1
  • 66
    • 0036742814 scopus 로고    scopus 로고
    • A stochastic projection method for fluid flow. II: Random process
    • LeMaitre O., Reagan M., Najm H., Ghanem R., Knio O. A stochastic projection method for fluid flow. II: Random process. J. Comput. Phys. 2002, 181:9-44.
    • (2002) J. Comput. Phys. , vol.181 , pp. 9-44
    • LeMaitre, O.1    Reagan, M.2    Najm, H.3    Ghanem, R.4    Knio, O.5
  • 67
    • 0025841017 scopus 로고
    • Accurate solutions to the square thermally driven cavity at high Rayleigh number
    • Quéré P.L. Accurate solutions to the square thermally driven cavity at high Rayleigh number. Comput. Fluids 1991, 20(1):29-41.
    • (1991) Comput. Fluids , vol.20 , Issue.1 , pp. 29-41
    • Quéré, P.L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.