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AAC+

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ABC+23

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AHL+14

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AA09

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ALG+00

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BT04

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BES+07

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BES+08

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BS11

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BJW17

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CDW14

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CEP12

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CG14

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CGI10

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CBRV13

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CKN06

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CT06

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DS14

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DVM+14

Christian Daniel, Malte Viering, Jan Metz, Oliver Kroemer, and Jan Peters. Active reward learning. In Robotics: Science and Systems. 2014.

DMA97

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DM97

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DT94

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DKB14

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DKS13

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DP10

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DO11

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DFG99

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DC04

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DWB05

Marco F. Duarte, Michael B. Wakin, and Richard G. Baraniuk. Fast reconstruction of piecewise smooth signals from random projections. In Online Proceedings of the Workshop on Signal Processing with Adaptative Sparse Structured Representations (SPARS). Rennes, France, 2005.

DH09

R.P. Dwight and Z. Han. Efficient uncertainty quantification using gradient-enhanced kriging. In 11th AIAA Non-Deterministic Approaches Conference. Reston, VA, USA, May 2009. American Institute of Aeronautics and Astronautics.

EMS+16

Mohamed S Ebeida, Scott A Mitchell, Laura P Swiler, Vicente J Romero, and Ahmad A Rushdi. Pof-darts: geometric adaptive sampling for probability of failure. Reliability Engineering & System Safety, 155:64–77, 2016.

EPH09

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EL01

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EHJT04

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ES09

M. S Eldred and L. P. Swiler. Efficient algorithms for mixed aleatory-epistemic uncertainty quantification with application to radiation-hardened electronics. part 1: algorithms and benchmark results. Technical Report SAND2009-5805, Sandia National Laboratories, Albuquerque, NM, 2009.

Eld98

M. S. Eldred. Optimization strategies for complex engineering applications. Technical Report SAND98-0340, Sandia National Laboratories, Albuquerque, NM, 1998.

EAP+07

M. S. Eldred, H. Agarwal, V. M. Perez, S. F. Wojtkiewicz, Jr., and J. E. Renaud. Investigation of reliability method formulations in DAKOTA/UQ. Structure & Infrastructure Engineering: Maintenance, Management, Life-Cycle Design & Performance, 3(3):199–213, 2007.

EB06

M. S. Eldred and B. J. Bichon. Second-order reliability formulations in DAKOTA/UQ. In Proceedings of the 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, number AIAA-2006-1828. Newport, RI, May 1–4 2006.

EB09

M. S. Eldred and J. Burkardt. Comparison of non-intrusive polynomial chaos and stochastic collocation methods for uncertainty quantification. In Proceedings of the 47th AIAA Aerospace Sciences Meeting and Exhibit, number AIAA-2009-0976. Orlando, FL, January 5–8, 2009.

ED06

M. S. Eldred and D. M. Dunlavy. Formulations for surrogate-based optimization with data fit, multifidelity, and reduced-order models. In Proceedings of the 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, number AIAA-2006-7117. Portsmouth, VA, September 6–8 2006.

EGC04

M. S. Eldred, A. A. Giunta, and S. S. Collis. Second-order corrections for surrogate-based optimization with model hierarchies. In Proceedings of the 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference. Albany, NY,, Aug. 30–Sept. 1, 2004. AIAA Paper 2004-4457.

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EH98

M. S. Eldred and W. E. Hart. Design and implementation of multilevel parallel optimization on the Intel TeraFLOPS. In Proc. 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, number AIAA-98-4707, 44–54. St. Louis, MO, September 2–4 1998.

EHB+96

M. S. Eldred, W. E. Hart, W. J. Bohnhoff, V. J. Romero, S. A. Hutchinson, and A. G. Salinger. Utilizing object-oriented design to build advanced optimization strategies with generic implementation. In Proc. 6th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, number AIAA-96-4164, 1568–1582. Bellevue, WA, September 4–6 1996.

EHSvanBWaanders00

M. S. Eldred, W. E. Hart, B. D. Schimel, and B. G. van Bloemen Waanders. Multilevel parallelism for optimization on MP computers: theory and experiment. In Proc. 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, number AIAA-2000-4818. Long Beach, CA, 2000.

EOB+96

M. S. Eldred, D. E. Outka, W. J. Bohnhoff, W. R. Witkowski, V. J. Romero, E. R. Ponslet, and K. S. Chen. Optimization of complex mechanics simulations with object-oriented software design. Computer Modeling and Simulation in Engineering, August 1996.

ES99

M. S. Eldred and B. D. Schimel. Extended parallelism models for optimization on massively parallel computers. In Proc. 3rd World Congress of Structural and Multidisciplinary Optimization (WCSMO-3), number 16-POM-2. Amherst, NY, May 17–21 1999.

EWC08

M. S. Eldred, C. G. Webster, and P. Constantine. Evaluation of non-intrusive approaches for wiener-askey generalized polynomial chaos. In Proceedings of the 10th AIAA Non-Deterministic Approaches Conference, number AIAA-2008-1892. Schaumburg, IL, April 7–10 2008.

EAG+07

M.S. Eldred, B.M. Adams, D.M. Gay, L.P. Swiler, K. Haskell, W.J. Bohnhoff, J.P. Eddy, W.E. Hart, J.P Watson, J.D. Griffin, P.D. Hough, T.G. Kolda, P.J. Williams, and M.L. Martinez-Canales. Dakota version 4.1 users manual. Sandia Technical Report SAND2006-6337, Sandia National Laboratories, Albuquerque, NM, 2007. URL: http://dakota.sandia.gov/licensing/release/Users4.1.pdf.

FRB90

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FDKI17

H.R. Fairbanks, A. Doostan, C. Ketelsen, and G. Iaccarino. A low-rank control variate for multilevel monte carlo simulation of high-dimensional uncertain systems. Journal of Computational Physics, 341:121–139, 2017.

FT06

S. Ferson and W. T. Tucker. Sensitivity analysis using probability bounding. Reliability Engineering and System Safety, 91:1435–1442, 2006.

Fla

D. Flaggs. JPrePost user's manual. In preparation.

FJ10

J. M. Flegal and G. L. Jones. Batch means and spectral variance estimators in Markov chain Monte Carlo. The Annals of Statistics, 38(2):1034–1070, 2010.

FLT02

R. Fletcher, S. Leyffer, and P. L. Toint. On the global convergence of a filter-SQP algorithm. SIAM J. Optim., 13(1):44–59, 2002.

FGK03

R. Fourer, D. M. Gay, and B. W. Kernighan. AMPL: A Modeling Language for Mathematical Programming, 2nd ed. Duxbury Press/Brooks/Cole Publishing Co., Pacific Grove, CA, 2003. For small examples, e.g., at most 300 variables, a student version of AMPL suffices; see \texttt http://www.ampl.com/DOWNLOADS.

FST05

P. Frauenfelder, C. Schwab, and R. A. Todor. Finite elements for elliptic problems with stochastic coefficients. Comput. Methods Appl. Mech. Engrg., 194(2-5):205–228, 2005.

Fri91

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Gab01

J. Gablonsky. Direct version 2.0 userguide technical report. Technical Report CRSC-TR01-08, North Carolina State University, Center for Research in Scientific Computation, Raleigh, NC, 2001.

GVSG14

S. Gao, G. Ver Steeg, and A Galstyan. Efficient estimation of mutual information for strongly dependent variables. CoRR, 2014. URL: http://arxiv.org/abs/1411.2003, arXiv:1411.2003.

Gau04

W. Gautschi. Orthogonal Polynomials: Computation and Approximation. Oxford University Press, New York, 2004.

Gay97

D. M. Gay. Hooking your solver to AMPL. Technical Report Technical Report 97-4-06, Bell Laboratories, Murray Hill, NJ, 1997. Available online as http://www.ampl.com/REFS/HOOKING/index.html and http://www.ampl.com/REFS/hooking2.pdf and http://www.ampl.com/REFS/hooking2.ps.gz.

GIE15

G. Geraci, G. Iaccarino, and Michael S. Eldred. A multi fidelity control variate approach for the multilevel monte carlo technique. CTR Annual Research Briefs 2015, pages 169–181, 2015.

GEI17

Gianluca Geraci, Michael S. Eldred, and Gianluca Iaccarino. A multifidelity multilevel Monte Carlo method for uncertainty propagation in aerospace applications. In 19th AIAA Non-Deterministic Approaches Conference. AIAA, January 2017. URL: http://arc.aiaa.org/doi/10.2514/6.2017-1951 (visited on 2019-10-04), doi:10.2514/6.2017-1951.

GG98

T. Gerstner and M. Griebel. Numerical integration using sparse grids. Numer. Algorithms, 18(3-4):209–232, 1998.

GG03

T. Gerstner and M. Griebel. Dimension-adaptive tensor-product quadrature. Computing, 71(1):65–87, 2003.

GRH99

R. Ghanem and J. R. Red-Horse. Propagation of probabilistic uncertainty in complex physical systems using a stochastic finite element technique. Physica D, 133:137–144, 1999.

GS91

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Gil08

Michael B. Giles. Multilevel Monte Carlo Path Simulation. Operations Research, 56(3):607–617, June 2008. URL: http://pubsonline.informs.org/doi/abs/10.1287/opre.1070.0496, doi:10.1287/opre.1070.0496.

Gil15

Michael B. Giles. Multilevel monte carlo methods. Acta Numerica, 24:259–328, 2015. doi:10.1017/S096249291500001X.

GRS98

W.R. Gilks, S. Richardson, and D.J. Spiegelhalter. Markov chain Monte Carlo in practice. Chapman & Hall, 1998.

GMSW86

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GRC10

David Ginsbourger, Rodolphe Riche, and Laurent Carraro. Kriging is well-suited to parallelize optimization. In Yoel Tenne and Chi-Keong Goh, editors, Computational Intelligence in Expensive Optimization Problems, volume 2 of Adaptation, Learning, and Optimization, pages 131–162. Springer Berlin Heidelberg, 2010. URL: http://dx.doi.org/10.1007/978-3-642-10701-6_6, doi:10.1007/978-3-642-10701-6_6.

Giu02

A. A. Giunta. Use of data sampling, surrogate models, and numerical optimization in engineering design. In Proc. 40th AIAA Aerospace Science Meeting and Exhibit, number AIAA-2002-0538. Reno, NV, January 2002.

GE00

A. A. Giunta and M. S. Eldred. Implementation of a trust region model management strategy in the DAKOTA optimization toolkit. In Proc. 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, number AIAA-2000-4935. Long Beach, CA, September 6–8, 2000.

GMSE06

A. A. Giunta, J. M. McFarland, L. P. Swiler, and M. S. Eldred. The promise and peril of uncertainty quantification using respone surface approximations. Structure and Infrastructure Engineering, 2(3-4):175–189, September-December 2006.

GSB+06

A. A. Giunta, L. P. Swiler, S. L Brown, M. S. Eldred, M. D. Richards, and E. C. Cyr. The surfpack software library for surrogate modeling of sparse, irregularly spaced multidimensional data. In Proceedings of the 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, number AIAA-2006-7049. Portsmouth, VA, 2006.

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L. P Swiler, R. Slepoy, and A. A. Giunta. Evaluation of sampling methods in constructing response surface approximations. In Proc. 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, number AIAA-2006-1827. Newport, RI, May 1-4 2006.

SW10

L. P. Swiler and N. J. West. Importance sampling: promises and limitations. In Proceedings of the 12th AIAA Non-Deterministic Approaches Conference, number AIAA-2010-2850. 2010.

SW04

L. P. Swiler and G. D. Wyss. A user's guide to Sandia's latin hypercube sampling software: LHS UNIX library and standalone version. Technical Report SAND04-2439, Sandia National Laboratories, Albuquerque, NM, July 2004.

TIE10

G. Tang, G. Iaccarino, and M. S Eldred. Global sensitivity analysis for stochastic collocation expansion. In Proceedings of the 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (12th AIAA Non-Deterministic Approaches conference). Orlando, FL, April 12-15, 2010. AIAA Paper 2010-XXXX.

TSE10

G. Tang, L. P. Swiler, and M. S Eldred. Using stochastic expansion methods in evidence theory for mixed aleatory-epistemic uncertainty quantification. In Proceedings of the 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (12th AIAA Non-Deterministic Approaches conference). Orlando, FL, April 12-15, 2010. AIAA Paper 2010-XXXX.

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Robert Tibshirani. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society, Series B, 58:267–288, 1996.

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Ramakrishna Tipireddy and Roger Ghanem. Basis adaptation in homogeneous chaos spaces. Journal of Computational Physics, 259:304 – 317, 2014. URL: http://www.sciencedirect.com/science/article/pii/S0021999113008085, doi:https://doi.org/10.1016/j.jcp.2013.12.009.

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TEW+22

Anh Tran, Mike Eldred, Tim Wildey, Scott McCann, Jing Sun, and Robert J Visintainer. aphBO-2GP-3B: a budgeted asynchronous parallel multi-acquisition functions for constrained Bayesian optimization on high-performing computing architecture. Structural and Multidisciplinary Optimization, 65(4):1–45, 2022.

TSF+19

Anh Tran, Jing Sun, John M Furlan, Krishnan V Pagalthivarthi, Robert J Visintainer, and Yan Wang. pBO-2GP-3B: A batch parallel known/unknown constrained Bayesian optimization with feasibility classification and its applications in computational fluid dynamics. Computer Methods in Applied Mechanics and Engineering, 347:827–852, 2019.

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VtBD+09

J. A. Vrugt, C. J. F. ter Braak, C. G. H. Diks, B. A. Robinson, J. M. Hyman, and D. Higdon. Accelerating Markov chain Monte Carlo simulation by self-adaptive differential evolution with randomized subspace sampling. International Journal of Nonlinear Scientific Numerical Simulation, 2009.

VSR+07

K. W. Vugrin, L. P. Swiler, R. M. Roberts, N. J. Stuckey-Mack, and S. P Sullivan. Confidence region estimation techniques for nonlinear regression in groundwater flow: three case studies. Water Resources Research, 2007.

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R. W. Walters. Towards stochastic fluid mechanics via polynomial chaos. In Proceedings of the 41st AIAA Aerospace Sciences Meeting and Exhibit, number AIAA-2003-0413. Reno, NV, January 6–9, 2003.

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Larry Wasserman. Bayesian model selection and model averaging. Journal of mathematical psychology, 44(1):92–107, 2000.

WEM06

G. Weickum, M. S. Eldred, and K. Maute. Multi-point extended reduced order modeling for design optimization and uncertainty analysis. In Proceedings of the 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (2nd AIAA Multidisciplinary Design Optimization Specialist Conference). Newport, RI, May 1–4, 2006. AIAA Paper 2006-2145.

WKS+12

V. G. Weirs, J. R. Kamm, L. P. Swiler, M. Ratto, S. Tarantola, B. M. Adams, W. J. Rider, and M. S Eldred. Sensitivity analysis techniques applied to a system of hyperbolic conservation laws. Reliability Engineering and System Safety, 107:157–170, 2012.

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J. A. S. Witteveen and H. Bijl. Modeling arbitrary uncertainties using gram-schmidt polynomial chaos. In Proceedings of the 44th AIAA Aerospace Sciences Meeting and Exhibit, number AIAA-2006-0896. Reno, NV, January 9–12 2006.

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Y.-T. Wu, Y. Shin, R. Sues, and M. Cesare. Safety-factor based approach for probability-based design optimization. In Proc. 42nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, number AIAA-2001-1522. Seattle, WA, April 16–19 2001.

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WR98a

B. A. Wujek and J. E. Renaud. New adaptive move-limit management strategy for approximate optimization, part 1. AIAA Journal, 36(10):1911–1921, 1998.

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B. A. Wujek and J. E. Renaud. New adaptive move-limit management strategy for approximate optimization, part 2. AIAA Journal, 36(10):1922–1934, 1998.

WJ98

G. D. Wyss and K. H. Jorgensen. A user's guide to LHS: Sandia's Latin hypercube sampling software. Technical Report SAND98-0210, Sandia National Laboratories, Albuquerque, NM, 1998.

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D. Xiu. Numerical integration formulas of degree two. Applied Numerical Mathematics, 58:1515–1520, 2008.

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S. Xu and R. V. Grandhi. Effective two-point function approximation for design optimization. AIAA J., 36(12):2269–2275, 1998.

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D. C. Zimmerman. Genetic algorithms for navigating expensive and complex design spaces. September 1996. Final Report for Sandia National Laboratories contract AO-7736 CA 02.

ZH05

Hui Zou and Trevor Hastie. Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67(2):301–320, 2005. URL: http://dx.doi.org/10.1111/j.1467-9868.2005.00503.x, doi:10.1111/j.1467-9868.2005.00503.x.

ZMR04

T. Zou, S. Mahadevan, and R. Rebba. Computational efficiency in reliability-based optimization. In Proceedings of the 9th ASCE Specialty Conference on Probabilistic Mechanics and Structural Reliability. Albuquerque, NM, July 26–28, 2004.

ZMMM02

T. Zou, Z. Mourelatos, S. Mahadevan, and P. Meernik. Reliability analysis of automotive body-door subsystem. Rel. Eng. and Sys. Safety, 78:315–324, 2002.

LeDigabel11

S. Le Digabel. Algorithm 909: NOMAD: nonlinear optimization with the MADS algorithm. ACM Transactions on Mathematical Software, 37(4):1–15, 2011.

NationalRCotNAcademies08

National Research Council of the National Academies. Evaluation of Quantification of Margins and Uncertainties Methodology for Assessing and Certifying the Reliability of the Nuclear Stockpile. National Academy Press, Washington D.C., 2008.