Issues in Deciding Whether to Use Multifidelity Surrogates

Fernández-Godino, M. Giselle; Park, Chanyoung; Kim, Nam Hoon; Haftka, Raphael T.

doi:10.2514/1.j057750

Cited by 166 publications

(68 citation statements)

References 146 publications

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“…However, the correlation between fidelities depends on the specific problem at hand. Fernández‐Godino et al 28 mentioned that there are different types of fidelities associated with three categories. The first is simplifying the mathematical model of the physical problem, like using a low‐fidelity flow solver, simplified geometry, or simplified boundary condition.…”

Section: Discussionmentioning

confidence: 99%

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Multi‐fidelity surrogate reduced‐order modeling of steady flow estimation

Wang

Kou

Zhang

2020

Numerical Methods in Fluids

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Summary A multi‐fidelity reduced‐order model (ROM), which incorporates low‐fidelity data to improve the prediction of high‐fidelity results, is proposed for the reconstruction of steady flow field at different conditions. The spatial basis functions of low‐fidelity and high‐fidelity data, which are generated for all training sets are extracted separately by proper orthogonal decomposition. Then a surrogate model is used to construct mappings between the mode coefficients obtained from low‐fidelity and the high‐fidelity data. In the online stage, both the low‐fidelity flow at the predicted state and the surrogate model are needed to predict the mode coefficients of the high‐fidelity flow, and the high‐fidelity flow field is subsequently reconstructed. This method differs from existing surrogate‐based reduced‐order modeling method because it allows the use of partial physical information for flow estimation, which is coming from the low‐fidelity data instead of adopting a black‐box mapping between system state and the projection coefficients. Numerical studies are presented for a lid‐driven cavity problem and transonic flow past a NACA0012 airfoil. Two low‐fidelity models, with either a coarse mesh or a lower numerical order, are considered respectively. Results show that the proposed multi‐fidelity ROM predicts the flow field accurately and outperforms the traditional methods in both interpolated and extrapolated conditions.

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Section: Discussionmentioning

confidence: 99%

“…Fusing data from multiple sources is often achieved by multi‐fidelity methods 27,28 . Multi‐fidelity methods combine high‐fidelity models and low‐fidelity models to obtain accurate high‐fidelity estimation at a reasonable cost.…”

Section: Introductionmentioning

confidence: 99%

Multi‐fidelity surrogate reduced‐order modeling of steady flow estimation

Wang

Kou

Zhang

2020

Numerical Methods in Fluids

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“…The multiplicative correction approach is an MFS option that is not included in this paper, however the reader can refer to [11] if interested. This MFS is constructed using as training points the quotient between y HF (x) and y LF (x) functions at the nested training data points.…”

Section: The Multi-fidelity Surrogatesmentioning

confidence: 99%

“…LR-MFS, as co-Kriging, corrects the LF model using a multiplicative constant plus a discrepancy function between LF and HF models. A second comparison was made by using additive Kriging [11], which is using Kriging surrogate to model the discrepancy between the LF and HF models using also exact LF simulations. In this approach, unlike in co-Kriging and LR-MFS, the LF model is not corrected using a multiplicative factor.…”

Section: Introductionmentioning

confidence: 99%

Linear regression-based multifidelity surrogate for disturbance amplification in multiphase explosion

Fernández-Godino

Dubreuil

Bartoli

et al. 2019

Struct Multidisc Optim

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When simulations are very expensive and many are required, as for optimization or uncertainty quantification, a way to reduce cost is using surrogates. With multiple simulations to predict the quantity of interest, some being very expensive and accurate (high-fidelity simulations) and others cheaper but less accurate (low-fidelity simulations), it may be worthwhile to use multi-fidelity surrogates (MFS). Moreover, if we can afford just a few high-fidelity simulations or experiments, MFS become necessary. Co-Kriging, which is probably the most popular MFS, replaces both lowfidelity and high-fidelity simulations by a single MFS. A recently proposed linear-regression-based MFS (LR-MFS) offers the option to correct the LF simulations instead of correcting the LF surrogate in the MFS. When the low-fidelity simulation is cheap enough for use in an application, such as optimization, this may be an attractive option. In this paper, we explore the performance of LR-MFS using exact and surrogate-replaced low-fidelity simulations. The problem studied is a cylindrical dispersal of 100µm diameter solid particles after detonation and the quantity of interest is a measure of the amplification of the departure from axisymmetry. We find very substantial accuracy improvements for this problem using the LR-MFS with exact low-fidelity simulations. Inspired by these results we also compare the per

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“…Further reductions of computational time can be achieved by combining models with various levels of fidelity during the optimization. Such so-called multi-fidelity (MF) models [28,29] leverage the use of inexpensive, but low-fidelity (LF) models for efficiently exploring the design or stochastic spaces, while using parsimonious high-fidelity (HF) samples to improve model accuracy. Examples of LF models are given by coarse-grid approximations [30][31][32][33], data-fit interpolation and regression models [34], projection-based reduced models [35,36], machine-learning-based models [37], or simplified models relying on approximations of the underlying physics [38][39][40].…”

Section: Introductionmentioning

confidence: 99%

Multi-Fidelity Gradient-Based Strategy for Robust Optimization in Computational Fluid Dynamics

Serafino

Obert²,

Cinnella

2020

Algorithms

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Efficient Robust Design Optimization (RDO) strategies coupling a parsimonious uncertainty quantification (UQ) method with a surrogate-based multi-objective genetic algorithm (SMOGA) are investigated for a test problem in computational fluid dynamics (CFD), namely the inverse robust design of an expansion nozzle. The low-order statistics (mean and variance) of the stochastic cost function are computed through either a gradient-enhanced kriging (GEK) surrogate or through the less expensive, lower fidelity, first-order method of moments (MoM). Both the continuous (non-intrusive) and discrete (intrusive) adjoint methods are evaluated for computing the gradients required for GEK and MoM. In all cases, the results are assessed against a reference kriging UQ surrogate not using gradient information. Subsequently, the GEK and MoM UQ solvers are fused together to build a multi-fidelity surrogate with adaptive infill enrichment for the SMOGA optimizer. The resulting hybrid multi-fidelity SMOGA RDO strategy ensures a good tradeoff between cost and accuracy, thus representing an efficient approach for complex RDO problems.

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Issues in Deciding Whether to Use Multifidelity Surrogates

Cited by 166 publications

References 146 publications

Multi‐fidelity surrogate reduced‐order modeling of steady flow estimation

Multi‐fidelity surrogate reduced‐order modeling of steady flow estimation

Linear regression-based multifidelity surrogate for disturbance amplification in multiphase explosion

Multi-Fidelity Gradient-Based Strategy for Robust Optimization in Computational Fluid Dynamics

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