Rapid Multi-Objective Aerodynamic Design Using Co-Kriging and Space Mapping

Kozieł, Sławomir; Tesfahunegn, Yonatan A.; Amrit, Anand; Leifsson, Leifur

doi:10.2514/6.2016-0418

Cited by 12 publications

(8 citation statements)

References 25 publications

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“…Yamazaki et al [39] used a gradient enhanced kriging to perform design optimization as well as uncertainty quantification at the optimal design point. Another optimization method known as space mapping [40][41][42][43] uses the low-fidelity models to solve an approximate optimization problem, where the input parameter space is mapped onto a different space to construct multi-fidelity models. Fischer et al [44] used a Bayesian approach for estimating weights of the low-fidelity models to be used for optimization in a multi-fidelity optimization setting.…”

Section: Multi-fidelity Models With Applications To Ouumentioning

confidence: 99%

Bi-fidelity Stochastic Gradient Descent for Structural Optimization under Uncertainty

Maute

Doostan

2019

Preprint

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The presence of uncertainty in material properties and geometry of a structure is ubiquitous. The design of robust engineering structures, therefore, needs to incorporate uncertainty in the optimization process. Stochastic gradient descent (SGD) method can alleviate the cost of optimization under uncertainty, which includes statistical moments of quantities of interest in the objective and constraints. However, the design may change considerably during the initial iterations of the optimization process which impedes the convergence of the traditional SGD method and its variants. In this paper, we present two SGD based algorithms, where the computational cost is reduced by employing a low-fidelity model in the optimization process. In the first algorithm, most of the stochastic gradient calculations are performed on the low-fidelity model and only a handful of gradients from the high-fidelity model are used per iteration, resulting in an improved convergence. In the second algorithm, we use gradients from low-fidelity models to be used as control variate, a variance reduction technique, to reduce the variance in the search direction. These two bi-fidelity algorithms are illustrated first with a conceptual example. Then, the convergence of the proposed bi-fidelity algorithms is studied with two numerical examples of shape and topology optimization and compared to popular variants of the SGD method that do not use low-fidelity models. The results show that the proposed use of a bi-fidelity approach for the SGD method can improve the convergence. Two analytical proofs are also provided that show the linear convergence of these two algorithms under appropriate assumptions.

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Section: Multi-fidelity Models With Applications To Ouumentioning

confidence: 99%

Bi-fidelity Stochastic Gradient Descent for Structural Optimization under Uncertainty

Maute

Doostan

2019

Preprint

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“…Reference Dimensionality [56] 2D/3D Eu, [81] 1D/3D RANS+TM, [84] 2D/3D URANS, [107] 2D/3D, [145] 1D/2D RANS, [156] 1D/2D Li, [175] 1D/3D RANS, [187] 1D/3D RANS, [203] 1D,2D/3D RANS Coarse/Refined [5] Eu, [25] RANS, [34] Eu, [35] Eu, [36] Li/Eu, [82] RANS, [88] MFF, [91] MHD, [98] Eu, [99], Eu [102] Eu, [115] Eu, [119] RANS, [153] RANS, [170] RANS, [196] [12] Li, [21] NL, [23] Li, [24] NL, [31] Li, [113] Li, [122] Li, [166] NL, [167] NL, [186] Li, [194] Li, [195] Li Boundary Conditions [182] Li, [185] Li [32] employed an iterative method that used LF surrogate models for approximating coupling variables and adaptive sampling of the HF system to refine the surrogates in order to maintain a similar level of accuracy as uncertainty propagation using the coupled HF multidisciplinary system.…”

Section: Fluid Mechanics Fidelity Typementioning

confidence: 99%

Review of multi-fidelity models

Fernández-Godino¹

2016

Preprint

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Simulations are often computationally expensive and the need for multiple realizations, as in uncertainty quantification or optimization, makes surrogate models an attractive option. For expensive high-fidelity models (HFMs), however, even performing the number of simulations needed for fitting a surrogate may be too expensive. Inexpensive but less accurate low-fidelity models (LFMs) are often also available. Multi-fidelity models (MFMs) combine HFMs and LFMs in order to achieve accuracy at a reasonable cost. With the increasing popularity of MFMs in mind, the aim of this paper is to summarize the state-of-the-art of MFM trends. For this purpose, publications in this field are classified based on application, surrogate selection if any, the difference between fidelities, the method used to combine these fidelities, the field of application and the year published.Available methods of combining fidelities are also reviewed, focusing our attention especially on multi-fidelity surrogate models in which fidelities are combined inside a surrogate model. Computation time savings are usually the reason for using MFMs, hence it is important to properly report the achieved savings. Unfortunately, we find that many papers do not present sufficient information to determine these savings. Therefore, the paper also includes guidelines for authors to present their MFM savings in a way that is useful to future MFM users. Based on papers that provided enough information, we find that time savings are highly problem dependent and that MFM methods we surveyed provided time savings up to 90%.

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“…This method, based on the physical process of molten metal cooling, is well-known for its ability of escaping local minima, although the results obtained can be highly dependent on the chosen metaparameters of the algorithm. Finally, it should be noted that for both gradient-based and gradient-free methods, a surrogate model can be used for the computational part, instead of systematically relying on a CFD solver [17]. Many methods to construct such surrogate models exist, such as radial basis functions, kriging, or supervised artificial neural networks [18].…”

Section: Introductionmentioning

confidence: 99%

“…In all these methods, the geometric parameterization plays a determinant role, both for the attainable geometries and for the tractability of the optimization process [19]. In particular, parameterizations based on Bézier curves [20], B-splines [17] and NURBS [21] have been widely studied within conventional optimization frameworks.…”

Section: Introductionmentioning

confidence: 99%

Direct shape optimization through deep reinforcement learning

Viquerat

Rabault

Kuhnle

et al. 2021

Journal of Computational Physics

134

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Deep Reinforcement Learning (DRL) has recently spread into a range of domains within physics and engineering, with multiple remarkable achievements. Still, much remains to be explored before the capabilities of these methods are well understood. In this paper, we present the first application of DRL to direct shape optimization. We show that, given adequate reward, an artificial neural network trained through DRL is able to generate optimal shapes on its own, without any prior knowledge and in a constrained time. While we choose here to apply this methodology to aerodynamics, the optimization process itself is agnostic to details of the use case, and thus our work paves the way to new generic shape optimization strategies both in fluid mechanics, and more generally in any domain where a relevant reward function can be defined.

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Rapid Multi-Objective Aerodynamic Design Using Co-Kriging and Space Mapping

Cited by 12 publications

References 25 publications

Bi-fidelity Stochastic Gradient Descent for Structural Optimization under Uncertainty

Bi-fidelity Stochastic Gradient Descent for Structural Optimization under Uncertainty

Review of multi-fidelity models

Direct shape optimization through deep reinforcement learning

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