Multifidelity approaches for uncertainty quantification

被引：6
作者：
Biehler J. [1 ]
Mäck M. [2 ]
Nitzler J. [1 ,3 ]
Hanss M. [2 ]
Koutsourelakis P.-S. [3 ]
Wall W.A. [1 ]
机构：
[1] Institute for Computational Mechanics, Technical University of Munich, Munich
[2] Institute of Engineering and Computational Mechanics, University of Stuttgart, Stuttgart
[3] hip of Continuum Mechanics, Technical University of Munich, Munich
来源：
GAMM Mitteilungen | 2019年 / 42卷 / 02期
关键词：
Bayesian; multifidelity; possibilistic; uncertainty quantification;
D O I：
10.1002/gamm.201900008
中图分类号：
学科分类号：
摘要：
The aim of this paper is to give an overview of different multifidelity uncertainty quantification (UQ) schemes. Therefore, different views on multifidelity UQ approaches from a frequentist, Bayesian, and possibilistic perspective are provided and recent developments are discussed. Differences as well as similarities between the methods are highlighted and strategies to construct low-fidelity models are explained. In addition, two state-of-the-art examples to showcase the capabilities of these methods and the tremendous reduction of computational costs that can be achieved when using these approaches are provided. © 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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[1]  
Heroux M.A., Bartlett R.A., Howle V.E., Hoekstra R.J., Hu J.J., Kolda T.G., Lehoucq R.B., Long K.R., Pawlowski R.P., Phipps E.T., Salinger A.G., Thornquist H.K., Tuminaro R.S., Willenbring J.M., Williams A., Stanley K.S., ACM Trans. Math. Softw. (TOMS), 31, 3, (2005)
[2]  
Giles M.B., Oper. Res., 56, 3, (2008)
[3]  
Peherstorfer B., Cui T., Marzouk Y., Willcox K., Comput. Methods Appl. Mech. Eng., 300, (2016)
[4]  
Kennedy M.C., O'Hagan A., Biometrika, 87, 1, (2000)
[5]  
Perdikaris P., Raissi M., Damianou A., Lawrence N.D., Karniadakis G.E., Phys. Eng. Sci., 473, (2017)
[6]  
Koutsourelakis P.S., SIAM J. Sci. Comput., 31, (2009)
[7]  
Biehler J., Gee M.W., Wall W.A., Biomech. Model. Mechanobiol., 14, 3, (2015)
[8]  
Mack M., Hanss M., Proceeding of the ISMA/USD 2018, (2018)
[9]  
Mack M., Hanss M., ASCE-ASME J. Risk Uncertain. Eng. Syst. Part B: Mech. Eng., (2019)
[10]  
Peherstorfer B., Willcox K., Gunzburger M., Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization. TR16-1, (2016)
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