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Adaptive experimental design for multi-fidelity surrogate modeling of multi-disciplinary systems

dc.contributor.authorJakeman, John D.
dc.contributor.authorFriedman, Sam
dc.contributor.authorEldred, Michael S.
dc.contributor.authorTamellini, Lorenzo
dc.contributor.authorGorodetsky, Alex A.
dc.contributor.authorAllaire, Doug
dc.date.accessioned2022-05-06T17:28:02Z
dc.date.available2023-07-06 13:28:01en
dc.date.available2022-05-06T17:28:02Z
dc.date.issued2022-06-30
dc.identifier.citationJakeman, John D.; Friedman, Sam; Eldred, Michael S.; Tamellini, Lorenzo; Gorodetsky, Alex A.; Allaire, Doug (2022). "Adaptive experimental design for multi-fidelity surrogate modeling of multi-disciplinary systems." International Journal for Numerical Methods in Engineering 123(12): 2760-2790.
dc.identifier.issn0029-5981
dc.identifier.issn1097-0207
dc.identifier.urihttps://hdl.handle.net/2027.42/172303
dc.description.abstractWe present an adaptive algorithm for constructing surrogate models of multi-disciplinary systems composed of a set of coupled components. With this goal we introduce “coupling” variables with a priori unknown distributions that allow surrogates of each component to be built independently. Once built, the surrogates of the components are combined to form an integrated-surrogate that can be used to predict system-level quantities of interest at a fraction of the cost of the original model. The error in the integrated-surrogate is greedily minimized using an experimental design procedure that allocates the amount of training data, used to construct each component-surrogate, based on the contribution of those surrogates to the error of the integrated-surrogate. The multi-fidelity procedure presented is a generalization of multi-index stochastic collocation that can leverage ensembles of models of varying cost and accuracy, for one or more components, to reduce the computational cost of constructing the integrated-surrogate. Extensive numerical results demonstrate that, for a fixed computational budget, our algorithm is able to produce surrogates that are orders of magnitude more accurate than methods that treat the integrated system as a black-box.
dc.publisherJohn Wiley & Sons, Inc.
dc.subject.otherexperimental design
dc.subject.othermulti-disciplinary
dc.subject.othermulti-fidelity
dc.subject.othermulti-physics
dc.subject.othersurrogate
dc.subject.otheruncertainty quantification
dc.titleAdaptive experimental design for multi-fidelity surrogate modeling of multi-disciplinary systems
dc.typeArticle
dc.rights.robotsIndexNoFollow
dc.subject.hlbsecondlevelMechanical Engineering
dc.subject.hlbsecondlevelEngineering (General)
dc.subject.hlbtoplevelEngineering
dc.description.peerreviewedPeer Reviewed
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/172303/1/nme6958.pdf
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/172303/2/nme6958_am.pdf
dc.identifier.doi10.1002/nme.6958
dc.identifier.sourceInternational Journal for Numerical Methods in Engineering
dc.identifier.citedreferenceAmsallem D, Zahr MJ, Farhat C. Nonlinear model order reduction based on local reduced-order bases. Int J Numer Methods Eng. 2012; 92 ( 10 ): 891 - 916. doi: 10.1002/nme.437
dc.identifier.citedreferenceHaji-Ali A, Nobile F, Tamellini L, Tempone R. Multi-index stochastic collocation for random PDEs. Comput Methods Appl Mech Eng. 2016; 306: 95 - 122. doi: 10.1016/j.cma.2016.03.029
dc.identifier.citedreferenceBeck J, Tamellini L, Tempone R. IGA-based multi-index stochastic collocation for random PDEs on arbitrary domains. Comput Methods Appl Mech Eng. 2019; 351: 330 - 350. doi: 10.1016/j.cma.2019.03.042
dc.identifier.citedreferencePiazzola C, Tamellini L, Pellegrini R, Broglia R, Serani A, Diez M. Comparing multi-index stochastic collocation and multi-fidelity stochastic radial basis functions for forward uncertainty quantification of ship resistance. Eng Comput. 2022.
dc.identifier.citedreferenceHaji-Ali AL, Nobile F, Tamellini L, Tempone R. Multi-index stochastic collocation convergence rates for random PDEs with parametric regularity. Found Comput Math. 2016; 16 ( 6 ): 1555 - 1605. doi: 10.1007/s10208-016-9327-7
dc.identifier.citedreferenceSmetana K, Patera AT. Optimal local approximation spaces for component-based static condensation procedures. SIAM J Sci Comput. 2016; 38 ( 5 ): A3318 - A3356. doi: 10.1137/15M1009603
dc.identifier.citedreferenceEigel M, Gruhlke R. A local hybrid surrogate-based finite element tearing interconnecting dual-primal method for nonsmooth random partial differential equations. Int J Numer Methods Eng. 2021; 122 ( 4 ): 1001 - 1030. doi: 10.1002/nme.6571
dc.identifier.citedreferenceMu L, Zhang G. A domain decomposition model reduction method for linear convection-diffusion equations with random coefficients. SIAM J Sci Comput. 2019; 41 ( 3 ): A1984 - A2011. doi: 10.1137/18M1170601
dc.identifier.citedreferenceContreras AA, Mycek P, Le Maitre OP, Rizzi F, Debusschere B, Knio OM. Parallel domain decomposition strategies for stochastic elliptic equations Part B: accelerated Monte Carlo sampling with local PC expansions. SIAM J Sci Comput. 2018; 40 ( 4 ): C547 - C580. doi: 10.1137/17M1132197
dc.identifier.citedreferencePeherstorfer B, Butnaru D, Willcox K, Bungartz HJ. Localized discrete empirical interpolation method. SIAM J Sci Comput. 2014; 36 ( 1 ): A168 - A192. doi: 10.1137/130924408
dc.identifier.citedreferenceBuhr A, Iapichino L, Ohlberger M, Rave S, Schindler F, Smetana K. Localized Model Reduction for Parameterized Problems. Walter De Gruyter; 2019.
dc.identifier.citedreferenceChen Y, Jakeman J, Gittelson C, Xiu D. Local polynomial chaos expansion for linear differential equations with high dimensional random inputs. SIAM J Sci Comput. 2015; 37 ( 1 ): A79 - A102. doi: 10.1137/140970100
dc.identifier.citedreferenceGranas A, Dugundji J. Fixed Point Theory. Springer Monographs in Mathematics. New York, NY: Springer; 2003. doi: 10.1007/978-0-387-21593-8
dc.identifier.citedreferenceRogers J. DeMAID/GA-An enhanced design manager’s aid for intelligent decomposition; 2012.
dc.identifier.citedreferenceMarque-Pucheu S, Perrin G, Garnier J. Efficient sequential experimental design for surrogate modeling of nested codes. ESAIM PS. 2019; 23: 245 - 270. doi: 10.1051/ps/2018011
dc.identifier.citedreferenceChen X, Ng B, Sun Y, Tong C. A flexible uncertainty quantification method for linearly coupled multi-physics systems. J Comput Phys. 2013; 248: 383 - 401. doi: 10.1016/j.jcp.2013.04.009
dc.identifier.citedreferenceJakeman J, Eldred M, Xiu D. Numerical approach for quantification of epistemic uncertainty. J Comput Phys. 2010; 229 ( 12 ): 4648 - 4663. doi: 10.1016/j.jcp.2010.03.003
dc.identifier.citedreferenceChen X, Park EJ, Xiu D. A flexible numerical approach for quantification of epistemic uncertainty. J Comput Phys. 2013; 240: 211 - 224. doi: 10.1016/j.jcp.2013.01.018
dc.identifier.citedreferenceNarayan A, Jakeman JD. Adaptive Leja sparse grid constructions for stochastic collocation and high-dimensional approximation. SIAM/J Sci Comput. 2014; 36 ( 6 ): 2952 - 2983. doi: 10.1137/140966368
dc.identifier.citedreferenceErnst OG, Sprungk B, Tamellini L. On expansions and nodes for sparse grid collocation of lognormal elliptic PDEs. Arxiv e-prints 2019(1906.01252). Accepted. To appear on the Springer book “Sparse grids and application - Munich 2018 proceedings.
dc.identifier.citedreferenceBungartz HJ, Griebel M. Sparse grids. Acta Numer. 2004; 13: 1 - 123. doi: 10.1017/S0962492904000182
dc.identifier.citedreferenceNobile F, Tamellini L, Tempone R. Convergence of quasi-optimal sparse-grid approximation of Hilbert-space-valued functions: application to random elliptic PDEs. Numer Math. 2016; 134 ( 2 ): 343 - 388. doi: 10.1007/s00211-015-0773-y
dc.identifier.citedreferenceEigel M, Ernst OG, Sprungk B, Tamellini L. On the convergence of adaptive stochastic collocation for elliptic partial differential equations with affine diffusion. SIAM J Numer Anal. 2022.
dc.identifier.citedreferenceChkifa A, Cohen A, Schwab C. High-dimensional adaptive sparse polynomial interpolation and applications to parametric PDEs. Found Comput Math. 2014; 14 ( 4 ): 601 - 633. doi: 10.1007/s10208-013-9154-z
dc.identifier.citedreferenceJakeman JD. PyApprox: probabilistic analysis and approximation of data and simulation; 2021. https://sandialabs.github.io/pyapprox/index.html
dc.identifier.citedreferenceZaman K, Mahadevan S. Robustness-based design optimization of multidisciplinary system under epistemic uncertainty. AIAA J. 2013; 51 ( 5 ): 1021 - 1031. doi: 10.2514/1.J051372
dc.identifier.citedreferenceLi K, Allaire D. A compressed sensing approach to uncertainty propagation for approximately additive functions. Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference; 2016. 10.1115/DETC2016-60195
dc.identifier.citedreferenceReed R. The Superalloys: Fundamentals and Applications. Cambridge University Press; 2006.
dc.identifier.citedreferenceRasmussen CE, Williams CKI. Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning). MIT Press; 2005.
dc.identifier.citedreferenceSacks J, Welch WJ, Mitchell TJ, Wynn HP. Design and analysis of computer experiments. Stat Sci. 1989; 4 ( 4 ): 409 - 423.
dc.identifier.citedreferenceGhanem R, Spanos P. Stochastic Finite Elements: A Spectral Approach. Springer-Verlag; 1991.
dc.identifier.citedreferenceSudret B. Global sensitivity analysis using polynomial chaos expansions. Reliab Eng Syst Saf. 2008; 93 ( 7 ): 964 - 979. doi: 10.1016/i.ress.2007.04.002
dc.identifier.citedreferenceXiu D, Karniadakis G. The Wiener-Askey polynomial chaos for stochastic differential equations. SIAM J Sci Comput. 2002; 24 ( 2 ): 619 - 644. doi: 10.1137/S1064827501387826
dc.identifier.citedreferenceHarbrecht H, Jakeman J, Zaspel P. Cholesky-based experimental design for Gaussian process and kernel-based emulation and calibration. Commun Comput Phys. 2021; 29 ( 4 ): 1152 - 1185. doi: 10.4208/cicp.OA-2020-0060
dc.identifier.citedreferenceDoostan A, Validi A, Iaccarino G. Non-intrusive low-rank separated approximation of high-dimensional stochastic models. Comput Methods Appl Mech Eng. 2013; 263: 42 - 55. doi: 10.1016/j.cma.2013.04.003
dc.identifier.citedreferenceGorodetsky A, Jakeman J. Gradient-based optimization for regression in the functional tensor-train format. J Comput Phys. 2018; 374: 1219 - 1238. doi: 10.1016/j.jcp.2018.08.010
dc.identifier.citedreferenceOseledets IV. Tensor-train decomposition. SIAM J Sci Comput. 2011; 33 ( 5 ): 2295 - 2317. doi: 10.1137/090752286
dc.identifier.citedreferenceNobile F, Tempone R, Webster C. A sparse grid stochastic collocation method for partial differential equations with random input data. SIAM J Numer Anal. 2008; 46 ( 5 ): 2309 - 2345. doi: 10.1137/060663660
dc.identifier.citedreferenceXiu D, Hesthaven J. High-order collocation methods for differential equations with random inputs. SIAM J Sci Comput. 2005; 27 ( 3 ): 1118 - 1139. doi: 10.1137/040615201
dc.identifier.citedreferenceJakeman J, Roberts S. Local and dimension adaptive stochastic collocation for uncertainty quantification. In: Garcke J, Griebel M, eds. Sparse Grids and Applications. Lecture Notes in Computational Science and Engineering. Vol 88. Springer; 2013: 181 - 203.
dc.identifier.citedreferenceChen P, Quarteroni A, Rozza G. Comparison between reduced basis and stochastic collocation methods for elliptic problems. J Sci Comput. 2014; 59 ( 1 ): 187 - 216. doi: 10.1007/s10915-013-9764-2
dc.identifier.citedreferenceElman HC, Liao Q. Reduced basis collocation methods for partial differential equations with random coefficients. SIAM/ASA J Uncertain Quantif. 2013; 1 ( 1 ): 192 - 217. doi: 10.1137/120881841
dc.identifier.citedreferenceManzoni A, Pagani S, Lassila T. Accurate solution of Bayesian inverse uncertainty quantification problems combining reduced basis methods and reduction error models. SIAM/ASA J Uncertain Quantif. 2016; 4 ( 1 ): 380 - 412. doi: 10.1137/140995817
dc.identifier.citedreferenceRozza G, Huynh DBP, Patera AT. Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Arch Comput Methods Eng. 2008; 15 ( 3 ): 229. doi: 10.1007/s11831-008-9019-9
dc.identifier.citedreferenceZhu Y, Zabaras N. Bayesian deep convolutional encoder decoder networks for surrogate modeling and uncertainty quantification. J Comput Phys. 2018; 366: 415 - 447. doi: 10.1016/j.jcp.2018.04.018
dc.identifier.citedreferenceQin T, Chen Z, Jakeman J, Xiu D. Deep learning of parameterized equations with applications to uncertainty quantification. Int J Uncertain Quantif. 2021; 11 ( 2 ): 63 - 82. doi: 10.1615/Int.J.UncertaintyQuantification.2020034123
dc.identifier.citedreferenceArnst M, Ghanem R, Phipps E, Red-Horse J. Measure transformation and efficient quadrature in reduced-dimensional stochastic modeling of coupled problems. Int J Numer Methods Eng. 2012; 92 ( 12 ): 1044 - 1080. doi: 10.1002/nme.4368
dc.identifier.citedreferenceAmaral S, Allaire D, Willcox K. A decomposition-based approach to uncertainty analysis of feed-forward multicomponent systems. Int J Numer Methods Eng. 2014; 100 ( 13 ): 982 - 1005. doi: 10.1002/nme.4779
dc.identifier.citedreferenceConstantine P, Phipps E, Wildey T. Efficient uncertainty propagation for network multiphysics systems. Int J Numer Methods Eng. 2014; 99 ( 3 ): 183 - 202. doi: 10.1002/nme.4667
dc.identifier.citedreferenceSankararaman S, Mahadevan S. Likelihood-based approach to multidisciplinary analysis under uncertainty. J Mech Des. 2012; 134 ( 3 ). doi: 10.1115/1.4005619
dc.identifier.citedreferenceMittal A, Chen X, Tong CH, Iaccarino G. A flexible uncertainty propagation framework for general multiphysics systems. SIAM/ASA J Uncertain Quantif. 2016; 4 ( 1 ): 218 - 243. doi: 10.1137/140981411
dc.identifier.citedreferenceCarlberg K, Guzzetti S, Khalil M, Sargsyan K. The network uncertainty quantification method for propagating uncertainties in component-based systems. arXiv; 2020.
dc.identifier.citedreferenceChaudhuri A, Lam R, Willcox K. Multifidelity uncertainty propagation via adaptive surrogates in coupled multidisciplinary systems. AIAA J. 2018; 56 ( 1 ): 235 - 249. doi: 10.2514/1.J055678
dc.identifier.citedreferenceFriedman S, Isaac B, Ghoreishi SF, Allaire DL. Efficient decoupling of multiphysics systems for uncertainty propagation. Proc AIAA SciTech Forum. 2018. doi: 10.2514/6.2018-1661
dc.identifier.citedreferenceIsaac B, Friedman S, Allaire DL. Efficient approximation of coupling variable fixed point sets for decoupling multidisciplinary systems. Proc AIAA SciTech Forum. 2018. doi: 10.2514/6.2018-1908
dc.identifier.citedreferenceKyzyurova KN, Berger JO, Wolpert RL. Coupling computer models through linking their statistical emulators. SIAM/ASA J Uncertain Quantif. 2018; 6 ( 3 ): 1151 - 1171. doi: 10.1137/17M1157702
dc.identifier.citedreferenceSanson F, Maitre OL, Congedo PM. Systems of Gaussian process models for directed chains of solvers. Comput Methods Appl Mech Eng. 2019; 352: 32 - 55. doi: 10.1016/j.cma.2019.04.013
dc.identifier.citedreferenceJakeman J, Eldred M, Geraci G, Gorodetsky A. Adaptive multi-index collocation for uncertainty quantification and sensitivity analysis. Int J Numer Methods Eng. 2019; 121: 1314 - 1343.
dc.working.doiNOen
dc.owningcollnameInterdisciplinary and Peer-Reviewed


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