Sudjianto, On sequential sampling for global metamodeling in engineering design, in ASME 2002 : Proc. Sargsyan, Enhancing $\ell_1$-minimization estimates of polynomial chaos expansions using basis selection, J. ISUMA'90: First International Symposium on Uncertainty Modeling and Analysis, University of Maryland, 1990, pp. Homma, An importance quantification technique in uncertainty analysis for computer models, in Proc. Marrel, Numerical studies of the metamodel fitting and validation processes, Int. , Least angle and l$1$ penalized regression: A review, Stat. Doostan, Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies, J. Doostan, Coherence motivated sampling and convergence analysis of least squares polynomial chaos regression, Comput. Halton, On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals, Numer. Watson, Pitfalls of using a single criterion for selecting experimental designs, Internat. 41st AIAA Aerospace Sciences Meeting and Exhibit, AIAA-2003-0649, 2003. Eldred, et al., Overview of modern design of experiments methods for computational simulations, in Proc. Spanos, Stochastic Finite Elements: A Spectral Approach, Courier Corporation, 2003. Spanos, Stochastic Finite Elements-A Spectral Approach, Springer-Verlag, 1991 (re-edited by Dover Publications, Mineola, 2003). Geisser, The predictive sample reuse method with applications, J. Faure, Discrépance de suites associées à un système de numération (en dimension s), Acta Arith. Sudjianto, Design and Modeling for Computer Experiments, CRC Press, 2005. Tibshirani, Least angle regression, Ann. 26th IASTED International Conference on Modelling, Identification, and Control, ACTA Press, 2007, pp. dos Santos, Sequential designs for simulation experiments: Nonlinear regression metamodeling, in Proc. Dhaene, Efficient space-filling and non-collapsing sequential design strategies for simulation-based modeling, European J. Pettit, Polynomial chaos expansion with Latin hypercube sampling for estimating response variability, AIAA J. Tempone, Discrete least squares polynomial approximation with random evaluations-application to parametric and stochastic elliptic PDEs, ESAIM Math. Rai, A least-squares method for sparse low rank approximation of multivariate functions, SIAM/ASA J. Sudret, Adaptive sparse polynomial chaos expansion based on least angle regression, J. Sudret, An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis, Prob. Lemaire, Stochastic finite elements: A non intrusive approach by regression, Eur. Welch, Integrated circuit design optimization using a sequential strategy, IEEE Trans. It is shown that the optimal sequential design based on the $S$-value criterion yields accurate, stable, and computationally efficient PCEs.ġ. A comparative study between several state-of-the-art methods is performed on four numerical models with varying input dimensionality and computational complexity. A novel sequential adaptive strategy where the ED is enriched sequentially by capitalizing on the sparsity of the underlying metamodel is introduced. This paper is concerned with the problem of identifying an optimal ED that maximizes the accuracy of the surrogate model over the whole input space within a given computational budget. An efficient sampling strategy is then needed to generate an accurate PCE at low computational cost. A least-square minimization technique may be used to determine the coefficients of the sparse PCE by relying on the so-called experimental design (ED), i.e., the sample points where the original computational model is evaluated. In this context, sparse polynomial chaos expansions (PCEs) have been shown to be among the most promising methods because of their ability to model highly complex models at relatively low computational costs. Uncertainty quantification (UQ) has received much attention in the literature in the past decade.
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