Comparison of Adaptive Design Space Exploration Methods Applied to S-Duct CFD Simulation

Garbo, Andrea; German, Brian

doi:10.2514/6.2016-0416

Cited by 7 publications

(4 citation statements)

References 11 publications

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“…Following the terminology of [26], various open and closedloop adaptive DoEs are presented in this section. In contrast to static DoEs like Latin hypercube sampling (LHS), Halton sampling or full-factorial designs, these methods take advantage of prior knowledge that is incorporated into an error function e( ) , e ∶ ℝ d → ℝ , representing a prior belief of the response accuracy of a ROM for a specific problem at a parameter combination ∈ P .…”

Section: Adaptive Sampling Strategiesmentioning

confidence: 99%

Adaptive sampling strategies for reduced-order modeling

Karcher

Franz

2022

CEAS Aeronaut J

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Reduced-order models (ROMs) become increasingly popular in industrial design and optimization processes, since they allow to approximate expensive high fidelity computational fluid dynamics (CFD) simulations in near real-time. The quality of ROM predictions highly depends on the placement samples in the spanned parameter space. Adaptive sampling strategies allow to identify regions of interest, which feature e.g. nonlinear responses with respect to the parameters, and therefore enable the sensible placement of new samples. By introducing more samples in these regions, the ROM prediction accuracy should increase. In this contribution we investigate different adaptive sampling strategies based on cross-validation, Gaussian mean-squared error, two methods exploiting the CFD residual and a two manifold embedding methods. The performance of those strategies is evaluated and measured by their ability to successfully identify the regions of interest and the resulting sample placement in terms of different quantitative statistical values. We further discuss the reduction of the ROM prediction error over the adaptive sampling iterations and show that depending on the adaptive sampling strategy, the number of required samples can be reduced by 35–44% without deteriorating model quality compared to a Halton sequence sampling plan.

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Section: Adaptive Sampling Strategiesmentioning

confidence: 99%

Adaptive sampling strategies for reduced-order modeling

Karcher

Franz

2022

CEAS Aeronaut J

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“…Recommendations for new designs to be evaluated are obtained by optimizing some criterion (defined over the design space) that maximizes the information that can be gained about the function. Several criteria have been proposed and assessed for use in closed-loop settings [27][28][29]. In this paper, the maximum variance design [27] criterion is maximized over the design space in order to guide the search.…”

Section: Adaptive Sampling For the Canonical Engineering Problemmentioning

confidence: 99%

“…Several criteria have been proposed and assessed for use in closed-loop settings [27][28][29]. In this paper, the maximum variance design [27] criterion is maximized over the design space in order to guide the search. The criterion capitalizes on the idea that the best location to sample is the one with the largest uncertainty in the prediction.…”

Section: Adaptive Sampling For the Canonical Engineering Problemmentioning

confidence: 99%

Empirical Assessment of Deep Gaussian Process Surrogate Models for Engineering Problems

Rajaram¹,

Puranik²,

Renganathan

et al. 2021

Journal of Aircraft

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In recent years, multi-layered hierarchical compositions of the well-known and widely used Gaussian process models called deep Gaussian processes are finding use in the approximation of black-box functions. In this paper, the performance of deep Gaussian process models is empirically evaluated and compared against the well-established Gaussian process models with a special emphasis on engineering problems. The work draws conclusions through detailed comparisons in terms of metrics such as computational training cost, data requirement, predictive error, and robustness to the choice of the initial design of experiments. Additionally, the viability and robustness of Deep Gaussian process models for applications on practical engineering problems are analyzed through sensitivity to hyperparameters and scalability with respect to the input space dimensionality respectively. Finally, the models are also compared in an adaptive construction setting, where they are built sequentially by selecting points that maximize posterior variance. Experiments are conducted on canonical test functions with varying input dimensions, an engineering test function, and a practical transonic airfoil test case with a high-dimensional input space. The experiments suggest that deep Gaussian process models outperform traditional Gaussian process models in terms of accuracy at the cost of incurring a significantly higher computational expense for the training procedure. The sensitivity studies indicate that inducing points is the most important hyperparameter that affects deep Gaussian process performance and training time. This work empirically shows that deep Gaussian processes are promising candidates for problems that are known to be nonlinear, high-dimensional, and when limited training data is available.

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“…Recommendations for new designs to be evaluated are obtained by optimizing some criterion (defined over the design space) that maximizes the information that can be gained about the function. Several criteria have been proposed and assessed for use in closed-loop settings [19][20][21]. In this paper, the maximum variance design criterion is maximized over the design space in order to guide the search.…”

Section: E Adaptive Samplingmentioning

confidence: 99%

Deep Gaussian Process Enabled Surrogate Models for Aerodynamic Flows

Rajaram

Puranik

Renganathan

et al. 2020

AIAA Scitech 2020 Forum

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Deep Gaussian process (DGP) models are multi-layered hierarchical generalizations of the well-known Gaussian process (GP) models widely used to construct surrogate models of aerodynamic quantities of interest. Combining the desirable features of GP models and deep neural networks (DNN), DGP models are known to perform well when training data is scarce and the behavior of the system response is highly non-stationary. In this paper, the performance of DGP models is evaluated against GP models. Detailed comparisons are made and conclusions are drawn in terms of training time, data requirements, predictive error, and robustness to choice of training design of experiments, among other metrics. Additionally, sensitivity and scalability analyses are conducted for the DGP models to evaluate their usability. Finally, an adaptive construction of both models is presented, where the models are built sequentially by selecting points that maximize posterior variance. Several experiments are conducted with canonical test functions at varying input dimensions and a viscous transonic airfoil test case at 42 input dimensions. The experiments suggest that DGP models outperform traditional GP models in terms of accuracy but incur higher computational costs for training.

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Comparison of Adaptive Design Space Exploration Methods Applied to S-Duct CFD Simulation

Cited by 7 publications

References 11 publications

Adaptive sampling strategies for reduced-order modeling

Adaptive sampling strategies for reduced-order modeling

Empirical Assessment of Deep Gaussian Process Surrogate Models for Engineering Problems

Deep Gaussian Process Enabled Surrogate Models for Aerodynamic Flows

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