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Hadigol, Mohammad; Doostan, Alireza (2017)
Languages: English
Types: Preprint
Subjects: Statistics - Computation, Mathematics - Probability
As non-institutive polynomial chaos expansion (PCE) techniques have gained growing popularity among researchers, we here provide a comprehensive review of major sampling strategies for the least squares based PCE. Traditional sampling methods, such as Monte Carlo, Latin hypercube, quasi-Monte Carlo, optimal design of experiments (ODE), Gaussian quadratures, as well as more recent techniques, such as coherence-optimal and randomized quadratures are discussed. We also propose a hybrid sampling method, dubbed alphabetic-coherence-optimal, that employs the so-called alphabetic optimality criteria used in the context of ODE in conjunction with coherence-optimal samples. A comparison between the empirical performance of the selected sampling methods applied to three numerical examples, including high-order PCE's, high-dimensional problems, and low oversampling ratios, is presented to provide a road map for practitioners seeking the most suitable sampling technique for a problem at hand. We observed that the alphabetic-coherence-optimal technique outperforms other sampling methods, specially when high-order ODE are employed and/or the oversampling ratio is low.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • [1] C. M. ANDERSON-COOK, C. M. BORROR, AND D. C. MONTGOMERY, Response surface design evaluation and comparison, Journal of Statistical Planning and Inference, 139 (2009), pp. 629 - 641.
    • [2] A. B. ATASHGAH AND A. SEIFI, Optimal design of multi-response experiments using semi-definite programming, Optimization and Engineering, 10 (2008), pp. 75-90.
    • [3] A. ATKINSON, A. DONEV, AND R. TOBIAS, Optimum experimental designs, with SAS, Oxford University Press, 2007.
    • [4] A. C. ATKINSON AND A. N. DONEV, The construction of exact D-optimum experimental designs with application to blocking response surface designs, Biometrika, 76 (1989), pp. 515-526.
    • [5] I. BABU SˇKA, F. NOBILE, AND R. TEMPONE, A stochastic collocation method for elliptic partial differential equations with random input data, Tech. Rep. 05-47, The Institute for Computational Engineering and Sciences (ICES), University of Texas, Austin, 2005. http://www.ices.utexas.edu/research/reports/2005.php.
    • [6] I. BABU SˇKA, F. NOBILE, AND R. TEMPONE, A stochastic collocation method for elliptic partial differential equations with random input data, SIAM Journal on Numerical Analysis, 45 (2007), pp. 1005-1034.
    • [7] P. BARALDI, F. CADINI, F. MANGILI, AND E. ZIO, Model-based and data-driven prognostics under different available information, Probabilistic Engineering Mechanics, 32 (2013), pp. 66 - 79.
    • [8] G. BLATMAN, B. SUDRET, AND M. BERVEILLER, Quasi random numbers in stochastic finite element analysis, Mcanique & Industries, 8 (2007), pp. 289-297.
    • [9] G. BOX, J. HUNTER, AND W. HUNTER, Statistics for Experimenters: Design, Innovation, and Discovery, Wiley, 2nd ed., 2005.
    • [10] A. BROUDISCOU, R. LEARDI, AND R. PHAN-TAN-LUU, Genetic algorithm as a tool for selection of D-optimal design, Chemometrics and Intelligent Laboratory Systems, 35 (1996), pp. 105 - 116.
    • [11] L. BROWN, I. OLKIN, J. SACKS, AND H. P. WYNN (EDS.), Jack Kiefer. Collected Papers III. Design of Experiments, New York: Springer, 1985.
    • [12] E. BURNAEV, I. PANIN, AND B. SUDRET, Conformal and Probabilistic Prediction with Applications: 5th International Symposium, COPA 2016, Madrid, Spain, April 20-22, 2016, Proceedings, Springer International Publishing, Cham, 2016, ch. Effective Design for Sobol Indices Estimation Based on Polynomial Chaos Expansions, pp. 165-184.
    • [13] N. A. BUTLER, Optimal and orthogonal Latin hypercube designs for computer experiments, Biometrika, 88 (2001), pp. 847-857.
    • [14] R. E. CAFLISCH, Monte carlo and quasi-monte carlo methods, Acta numerica, 7 (1998), pp. 1-49.
    • [15] R. CAMERON AND W. MARTIN, The orthogonal development of nonlinear functionals in series of Fourier-Hermite functionals, Ann. Math., 48 (1947), pp. 385-392.
    • [16] X. CHEN, R. S. WOMERSLEY, AND J. J. YE, Minimizing the condition number of a gram matrix, SIAM Journal on optimization, 21 (2011), pp. 127-148.
    • [17] S. K. CHOI, R. CANFIELD, R. GRANDHI, AND C. PETTIT, Polynomial Chaos Expansion with Latin Hypercube Sampling for Estimating Response Variability, AIAA Journal, 42 (2004), pp. 1191-1198.
    • [18] A. COHEN, M. A. DAVENPORT, AND D. LEVIATAN, On the stability and accuracy of least squares approximations, Foundations of Computational Mathematics, 13 (2013), pp. 819-834.
    • [19] A. COHEN AND G. MIGLIORATI, Optimal weighted least-squares methods, arXiv preprint arXiv:1608.00512, (2016).
    • [20] P. CONSTANTINE, A. DOOSTAN, AND G. IACCARINO, A hybrid collocation/galerkin scheme for convective heat transfer problems with stochastic boundary conditions, International Journal for Numerical Methods in Engineering, 80 (2009), pp. 868-880.
    • [21] P. G. CONSTANTINE, M. ELDRED, AND E. PHIPPS, Sparse pseudospectral approximation method, Computer Methods in Applied Mechanics and Engineering, 229 (2012), pp. 1-12.
    • [22] R. D. COOK AND C. J. NACHTSHEIM, A comparison of algorithms for constructing exact D-optimal designs, Technometrics, 22 (1980), pp. 315-324.
    • [23] M. DAIGLE AND C. KULKARNI, Electrochemistry-based battery modeling for prognostics, in Annual Conference of the Prognostics and Health Management Society, October 2013, pp. 249-261.
    • [24] M. DAIGLE, A. SAXENA, AND K. GOEBEL, An efficient deterministic approach to model-based prediction uncertainty estimation, in: Annual Conference of the Prognostics and Health Management Society, (2012), pp. 326-335.
    • [25] H. DETTE AND Y. GRIGORIEV, E-optimal designs for second-order response surface models, Ann. Statist., 42 (2014), pp. 1635-1656.
    • [26] J. DICK AND F. PILLICHSHAMMER, Digital Nets and Sequences: Discrepancy Theory and Quasi-Monte Carlo Integration, Cambridge University Press, New York, NY, USA, 2010.
    • [27] A. DOOSTAN AND H. OWHADI, A non-adapted sparse approximation of PDEs with stochastic inputs, Journal of Computational Physics, 230 (2011), pp. 3015-3034.
    • [28] O. DYKSTRA, The augmentation of experimental data to maximize jx0xj, Technometrics, 13 (1971), pp. 682-688.
    • [29] K. ENTACHER, Discrepancy estimates based on haar functions, Mathematics and Computers in Simulation, 55 (2001), pp. 49 - 57. The Second fIMACSg Seminar on Monte Carlo Methods.
    • [30] D. FALLER, U. KLINGMLLER, AND J. TIMMER, Simulation methods for optimal experimental design in systems biology, Simulation, (2003), p. 2003.
    • [31] K. FANG, D. K. J. LIN, P. WINKER, AND Y. ZHANG, Uniform design: Theory and application, Technometrics, 42 (2000), pp. 237-248.
    • [32] K. T. FANG, The Uniform Design: Application of Number-Theoretic Methods in Experimental Design, Acta Mathematicae Applicatae Sinica 3(4) December 197, 3 (1980), pp. 363-372.
    • [33] K. T. FANG AND H. QIN, A note on construction of nearly uniform designs with large number of runs, Statistics & Probability Letters, 61 (2003), pp. 215 - 224.
    • [34] K. T. FANG, W.-C. SHIU, AND J.-X. PAN, Uniform designs based on Latin squares, Statistica Sinica, 9 (1999), pp. 905-912.
    • [35] K. T. FANG AND Y. WANG, Number-Theoretic Methods in Statistics, Chapman & Hall, London, 1994.
    • [36] V. FEDOROV, Theory of Optimal Experiments, Academic Press Inc, 1972.
    • [37] V. FEDOROV AND P. HACKL, Model-Oriented Design of Experiments, Springer-Verlag New York, 1997.
    • [38] J. D. FELDHACKER, B. A. JONES, A. DOOSTAN, AND J. HAMPTON, Reduced cost mission design using surrogate models, Advances in Space Research, 57 (2016), pp. 588-603.
    • [39] M. FORACCHIA, A. C. HOOKER, P. VICINI, AND A. RUGGERI, POPED, a software for optimal experiment design in population kinetics, Computer Methods and Programs in Biomedicine, 74 (2004).
    • [40] R. GHANEM AND P. SPANOS, Stochastic Finite Elements: A Spectral Approach, Springer Verlag, 1991.
    • [41] P. GOOS AND B. JONES, Optimal Design of Experiments: A Case Study Approach, Wiley, 2011.
    • [42] M. HADIGOL, K. MAUTE, AND A. DOOSTAN, On uncertainty quantification of lithium-ion batteries: Application to an Lic6/LiCoO2 cell, Journal of Power Sources, 300 (2015), pp. 507-524.
    • [43] L. M. HAINES, The application of the annealing algorithm to the construction of exact optimal designs for linear-regression models, Technometrics, 29 (1987), pp. 439-447.
    • [44] J. HAMPTON AND A. DOOSTAN, Coherence motivated sampling and convergence analysis of least squares polynomial chaos regression, Computer Methods in Applied Mechanics and Engineering, 290 (2015), pp. 73 - 97.
    • [45] , Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies, Journal of Computational Physics, 280 (2015), pp. 363 - 386.
    • [46] J. HAMPTON AND A. DOOSTAN, Compressive Sampling Methods for Sparse Polynomial Chaos Expansions, Springer International Publishing, 2016, pp. 1-29.
    • [47] P. C. HANSEN, V. PEREYRA, AND G. SCHERER, Least squares data fitting with applications, JHU Press, 2012.
    • [48] R. HARDIN AND N. SLOANE, A new approach to the construction of optimal designs, Journal of Statistical Planning and Inference, 37 (1993), pp. 339 - 369.
    • [49] R. H. HARDIN AND N. J. A. SLOANE, Gosset: A general-purpose program for designing experiments. http://www.NeilSloane.com/gosset.
    • [50] R. HOOKE AND T. A. JEEVES, Direct search solution of numerical and statistical problems, J. ACM, 8 (1961), pp. 212-229.
    • [51] S. HOSDER, R. WALTERS, AND R. PEREZ, A non-intrusive polynomial chaos method for uncertainty propagation in CFD simulations, in 44th AIAA aerospace sciences meeting and exhibit, AIAA-2006-891, Reno (NV), 2006.
    • [52] D. HUNTINGTON AND C. LYRINTZIS, Improvements to and limitations of Latin hypercube sampling, Probabilistic Engineering Mechanics, 13 (1998), pp. 245 - 253.
    • [53] R. L. IMAN AND W. J. CONOVER, A distribution-free approach to inducing rank correlation among input variables, Communications in Statistics - Simulation and Computation, 11 (1982), pp. 311-334.
    • [54] W. J. W. JEROME SACKS, SUSANNAH B. SCHILLER, Designs for computer experiments, Technometrics, 31 (1989), pp. 41-47.
    • [55] D. M. JIE YANG, ABHYUDAY MANDAL, Optimal designs for two-level factorial experiments with binary response, Statistica Sinica, 22 (2012), pp. 885-907.
    • [56] M. JOHNSON, L. MOORE, AND D. YLVISAKER, Minimax and maximin distance designs, Journal of Statistical Planning and Inference, 26 (1990), pp. 131 - 148.
    • [57] M. E. JOHNSON AND C. J. NACHTSHEIM, Some guidelines for constructing exact d-optimal designs on convex design spaces, Technometrics, 25 (1983), pp. 271-277.
    • [58] R. T. JOHNSON, B. JONES, J. W. FOWLER, AND D. C. MONTGOMERY, Comparing designs for computer simulation experiments, in Simulation Conference, 2008. WSC 2008. Winter, Dec 2008, pp. 463-470.
    • [59] R. T. JOHNSON, D. C. MONTGOMERY, B. JONES, AND P. A. PARKER, Comparing computer experiments for fitting high-order polynomial metamodels, Journal of Quality Technology, 42 (2010), pp. 86-102.
    • [60] B. JONES AND P. GOOS, I-optimal versus D-optimal split-plot response surface designs, Working Papers 2012002, University of Antwerp, Faculty of Applied Economics, Jan. 2012.
    • [61] B. A. JONES AND A. DOOSTAN, Satellite collision probability estimation using polynomial chaos expansions, Advances in Space Research, 52 (2013), pp. 1860 - 1875.
    • [62] V. R. JOSEPH, Space-filling designs for computer experiments: A review, Quality Engineering, 28 (2016), pp. 28-35.
    • [63] V. R. JOSEPH, E. GUL, AND S. BA, Maximum projection designs for computer experiments, Biometrika, 102 (2015), pp. 371-380.
    • [64] V. R. JOSEPH AND Y. HUNG, Orthogonal-maximin Latin hypercube designs, Statistica Sinica, 18 (2008), pp. 171-186.
    • [65] G. M. KABERA, L. M. HAINES, AND P. NDLOVU, The analytic construction of D-optimal designs for the two-variable binary logistic regression model without interaction, Statistics, 49 (2015), pp. 1169-1186.
    • [66] J. KIEFER, Optimum experimental designs, Journal of the Royal Statistical Society. Series B (Methodological), 21 (1959), pp. 272-319.
    • [67] J. P. C. KLEIJNEN, Design and Analysis of Simulation Experiments, Springer, 2008.
    • [68] G. LIMENG, P. JINGYUE, L. DATONG, AND P. XIYUAN, Data-driven framework for lithium-ion battery remaining useful life estimation based on improved nonlinear degradation factor, in Electronic Measurement Instruments (ICEMI), 2013 IEEE 11th International Conference on, vol. 2, Aug 2013, pp. 1014-1020.
    • [69] D. LIU, W. XIE, H. LIAO, AND Y. PENG, An integrated probabilistic approach to lithium-ion battery remaining useful life estimation, Instrumentation and Measurement, IEEE Transactions on, 64 (2015), pp. 660-670.
    • [70] W. J. C. M. D. MCKAY, R. J. BECKMAN, A comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics, 21 (1979), pp. 239-245.
    • [71] C. V. MAI AND B. SUDRET, Polynomial chaos expansions for damped oscillators, in ICASP12 12th International Conference on Applications of Statistics and Probability in Civil Engineering, Vancouver, Canada, 2015.
    • [72] O. L. MAITRE AND O. KNIO, Spectral Methods for Uncertainty Quantification with Applications to Computational Fluid Dynamics, Springer, 2010.
    • [73] A. MANDAL, W. K. WONG, AND Y. YU, Algorithmic searches for optimal designs, in Handbook of Design and Analysis of Experiments,
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