Multi-fidelity efficient global optimization: Methodology and application to airfoil shape design

Meliani, Mostafa; Bartoli, Nathalie; Lefèbvre, Thierry; Bouhlel, Mohamed-Amine; Martins, Joaquim R. R. A.; Morlier, Joseph

doi:10.2514/6.2019-3236

Cited by 22 publications

(12 citation statements)

References 23 publications

(34 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this case, however, either the LF or the HF model can be used for the infill. In the following calculations, we adopt the strategy of [42]: for the infill, priority is given to the less expensive LF model, and the HF one is used only when improvement achieved with the lower level of fidelity is below a given tolerance, tol = 10 −4 in the present calculations. Either way, re-sampling at the same location is avoided.…”

Section: Multi-fidelity Methods For Rdomentioning

confidence: 99%

“…A simple approach consists of linking the HF and the LF models by means of an additive correlation [41]: given an LF model f LF (ξ) and an HF model f HF (ξ), it is assumed that f HF (ξ) = f LF (ξ) + δ(ξ) where δ(ξ) is an error function to be estimated. This approach is accurate enough when HF and LF models have similar scales and a good correlation, as is the case for coarse-grid approximations [42]. As an alternative, a multiplicative correlation can be used [43][44][45]: f HF (ξ) = ρ(ξ) f LF (ξ), with ρ(ξ) a constant scalar multiplier.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Serafino

Obert²,

Cinnella

2020

Algorithms

View full text Add to dashboard Cite

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.

show abstract

Section: Multi-fidelity Methods For Rdomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Serafino

Obert²,

Cinnella

2020

Algorithms

View full text Add to dashboard Cite

show abstract

“…A body of literature proposes computational methods for multifidelity Bayesian optimization applied to aerospace design problems. Among that, Meliani et al (2019) developed a multifidelity Bayesian framework to increase the efficiency of optimization problems subjected to the curse of dimensionality, and demonstrate it for the optimization of a subsonic airfoil. Mondal et al (2019) implemented a multifidelity Bayesian strategy for the optimization of a transonic compressor rotor, where a reduced number of costly high-fidelity CFD evaluations are used to enrich a lowfidelity aerodynamic surrogate.…”

Section: Domain-aware Multifidelity Learningmentioning

confidence: 99%

Multifidelity domain-aware learning for the design of re-entry vehicles

Fiore

Maggiore

Mainini

2021

Struct Multidisc Optim

View full text Add to dashboard Cite

The multidisciplinary design optimization (MDO) of re-entry vehicles presents many challenges associated with the plurality of the domains that characterize the design problem and the multi-physics interactions. Aerodynamic and thermodynamic phenomena are strongly coupled and relate to the heat loads that affect the vehicle along the re-entry trajectory, which drive the design of the thermal protection system (TPS). The preliminary design and optimization of re-entry vehicles would benefit from accurate high-fidelity aerothermodynamic analysis, which are usually expensive computational fluid dynamic simulations. We propose an original formulation for multifidelity active learning that considers both the information extracted from data and domain-specific knowledge. Our scheme is developed for the design of re-entry vehicles and is demonstrated for the case of an Orion-like capsule entering the Earth atmosphere. The design process aims to minimize the mass of propellant burned during the entry maneuver, the mass of the TPS, and the temperature experienced by the TPS along the re-entry. The results demonstrate that our multifidelity strategy allows to achieve a sensitive improvement of the design solution with respect to the baseline. In particular, the outcomes of our method are superior to the design obtained through a single-fidelity framework, as a result of the principled selection of a limited number of high-fidelity evaluations.

show abstract

“…Therefore, the noisy observations directly propagate from level 2 to level 3, and the terminal estimation sees the noise of level 2 in the N-MF-method. The NN-MF-method uses instead observation residuals based on the mean prediction at the previous level, see (18). Substituting Y (l) ) smooths-out most of the noise in the observations of level 2 and limits its propagation to subsequent levels.…”

Section: Noisy Estimationsmentioning

confidence: 99%

“…Recently, the problem of applying EGO to airfoil shape optimization in a multi-fidelity framework was considered in [18]. Nested datasets are used to build MF-surrogates, and the Expected Improvement merit function is computed on the highest fidelity level.…”

Section: Introductionmentioning

confidence: 99%

A Non-Nested Infilling Strategy for Multifidelity Based Efficient Global Optimization

Sacher

Maître

Duvigneau

et al. 2021

Int. J. UncertaintyQuantification

View full text Add to dashboard Cite

Efficient Global Optimization (EGO) has become a standard approach for the global optimization of complex systems with high computational costs. EGO uses a training set of objective function values computed at selected input points to construct a statistical surrogate model, with low evaluation cost, on which the optimization procedure is applied. The training set is sequentially enriched, selecting new points, according to a prescribed infilling strategy, in order to converge to the optimum of the original costly model. Multi-fidelity approaches combining evaluations of the quantity of interest at different fidelity levels have been recently introduced to reduce the computational cost of building a global surrogate model. However, the use of multi-fidelity approaches in the context of EGO is still a research topic. In this work, we propose a new effective infilling strategy for multi-fidelity EGO. Our infilling strategy has the particularity of relying on non-nested training sets, a characteristic that comes with several computational benefits. For the enrichment of the multi-fidelity training set, the strategy selects the next input point together with the fidelity level of the objective function evaluation. This characteristic is in contrast with previous nested approaches, which require estimation all lower fidelity levels and are more demanding to update the surrogate. The resulting EGO procedure achieves a significantly reduced computational cost, avoiding computations at useless fidelity levels whenever possible, but it is also more robust to low correlations between levels and noisy estimations. Analytical problems are used to test and illustrate the efficiency of the method. It is finally applied to the optimization of a fully nonlinear fluid-structure interaction system to demonstrate its feasibility on real large-scale problems, with fidelity levels mixing physical approximations in the constitutive models and discretization refinements.

show abstract

Multi-fidelity efficient global optimization: Methodology and application to airfoil shape design

Cited by 22 publications

References 23 publications

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

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

Multifidelity domain-aware learning for the design of re-entry vehicles

A Non-Nested Infilling Strategy for Multifidelity Based Efficient Global Optimization

Contact Info

Product

Resources

About