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Multi-fidelity for MDO using Gaussian Processes

Abstract : Multi-fidelity models aim at combining models of different fidelities to achieve the desired accuracy at a lower computational cost. In Section 8.2, the connection between MDO, multi-fidelity and cokriging is made through a review of past works and system representations of code architectures. Then, the rest of this Chapter is divided into two main parts. First, in Section 8.3, a general model for cokriging is described that is based on the linear combination of independent (latent) processes. It is shown how, through its covariance structure, this model can represent all types of couplings between codes, whether they are serial (Markovian), fully coupled or parallel. Second, in Section 8.4, optimization approaches that use multiple outputs cokriging model are presented. They can work with any types of correlated outputs, including multi-fidelity outputs. They are generalizations of the EGO algorithm [Jones et al., 1998] where not only the next set of inputs but also the fidelity level changes at each iteration. The main method is called SoS for Step or Stop. The benefits brought by SoS are illustrated with a series of analytical test cases that mimic three typical type of multi-fidelity: mesh size variation in finite element like codes, number of samples in Monte Carlo simulations and time steps in dynamical systems.
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Submitted on : Wednesday, January 13, 2021 - 12:01:42 PM
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Nicolas Garland, Rodolphe Le Riche, Yann Richet, Nicolas Durrande. Multi-fidelity for MDO using Gaussian Processes. Loic Brevault; Mathieu Balesdent; Jerome Morio. Aerospace System Analysis and Optimization in Uncertainty, 156, Springer, pp.295-320, 2020, Springer Optimization and its Applications, 978-3-03 0-39126-3. ⟨10.1007/978-3-030-39126-3_8⟩. ⟨hal-02444005⟩

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