2019
DOI: 10.1002/gamm.201900008
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Multifidelity approaches for uncertainty quantification

Abstract: 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 … Show more

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Cited by 14 publications
(13 citation statements)
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“…Further research in this regard has been conducted and the means to reduce the computational effort have been developed, such as the elimination of recurring permutations, the treatment of single occurrences of variables through interval arithmetic, and automatic differentiation to test for monotonicity of a model as proposed by Klimke [13]. Recent extensions of the fuzzy arithmetic have been introduced by Mäck et al [14] to perform a structural optimization with uncertain constraints and finally to quantify the fuzziness of complex systems by using multifidelity approaches as shown by Biehler et al in [15].…”
Section: Discussionmentioning
confidence: 99%
“…Further research in this regard has been conducted and the means to reduce the computational effort have been developed, such as the elimination of recurring permutations, the treatment of single occurrences of variables through interval arithmetic, and automatic differentiation to test for monotonicity of a model as proposed by Klimke [13]. Recent extensions of the fuzzy arithmetic have been introduced by Mäck et al [14] to perform a structural optimization with uncertain constraints and finally to quantify the fuzziness of complex systems by using multifidelity approaches as shown by Biehler et al in [15].…”
Section: Discussionmentioning
confidence: 99%
“…For efficient time integration, the method used in the present work relies on well-known projection methods that segregate the solution of velocity and pressure unknowns, where the second-order accurate dual splitting scheme with an explicit treatment of the convective term is used here. 1 In all simulations, the same parameterized mesh according to Fehn et al 49 was used. The simulation domain and the mesh for one sample random input realization ∼ ( ) is shown in Figure 7 for the HF and the LF model version, respectively.…”
Section: Stochastic Flow Past a Cylinder: High-order Discontinuous Ga...mentioning
confidence: 99%
“…We select an initial sample size of N sample = 10000 for the LF model, so that the relative error E ∕ ̂ in the mean estimate is 1%. Afterwards, we successively compute features and choose five features to calculate a Ω × LF -filling subset [ LF ( ), ( )] ⊂ [ LF ( * ), ( * )] , with ∈ N ∶ [1,5]. We choose a data set of size n train = 150, corresponding to 150 HF model simulations to train the Gaussian Process model.…”
Section: Stochastic Flow Past a Cylinder: High-order Discontinuous Ga...mentioning
confidence: 99%
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“…Le Gratiet [9] introduced multiple ways to include information from different levels in a GP while Bieler et al [10] showed the technique for complex UQ scenarios. Le Gratiet [9] introduced multiple ways to include information from different levels in a GP while Bieler et al [10] showed the technique for complex UQ scenarios.…”
Section: Integration Of Multi-fidelity Informationmentioning
confidence: 99%