A multifidelity approach for the construction of explicit decision boundaries: application to aeroelasticity

Dribusch, Christoph; Missoum, Samy; Beran, Philip S.

doi:10.1007/s00158-010-0516-8

Cited by 30 publications

(15 citation statements)

References 23 publications

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“…In particular, kriging models are equipped with error indicators, see, e.g., [185]. There are also support vector machines [207,49,23,188], which have been developed by the machine-learning community for classification tasks but are now used as surrogates in science and engineering as well, see, e.g., [70,16,59,164].…”

Section: Types Of Low-fidelity Modelsmentioning

confidence: 99%

See 1 more Smart Citation

Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization

Peherstorfer¹,

Willcox²,

Gunzburger³

2018

SIAM Rev.

765

454

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In many situations across computational science and engineering, multiple computational models are available that describe a system of interest. These different models have varying evaluation costs and varying fidelities. Typically, a computationally expensive high-fidelity model describes the system with the accuracy required by the current application at hand, while lower-fidelity models are less accurate but computationally cheaper than the high-fidelity model. Outer-loop applications, such as optimization, inference, and uncertainty quantification, require multiple model evaluations at many different inputs, which often leads to computational demands that exceed available resources if only the high-fidelity model is used. This work surveys multifidelity methods that accelerate the solution of outer-loop applications by combining high-fidelity and low-fidelity model evaluations, where the low-fidelity evaluations arise from an explicit low-fidelity model (e.g., a simplified physics approximation, a reduced model, a data-fit surrogate, etc.) that approximates the same output quantity as the high-fidelity model. The overall premise of these multifidelity methods is that low-fidelity models are leveraged for speedup while the high-fidelity model is kept in the loop to establish accuracy and/or convergence guarantees. We categorize multifidelity methods according to three classes of strategies: adaptation, fusion, and filtering. The paper reviews multifidelity methods in the outer-loop contexts of uncertainty propagation, inference, and optimization.

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Section: Types Of Low-fidelity Modelsmentioning

confidence: 99%

“…An adaptive sampling scheme is introduced that refines the low-fidelity model along the failure boundary. In [59], another approach is introduced that uses a support vector machine to approximate the failure boundary. It is proposed to train the support vector machine with data obtained from a low-and a high-fidelity model.…”

Section: 4mentioning

confidence: 99%

Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization

Peherstorfer¹,

Willcox²,

Gunzburger³

2018

SIAM Rev.

765

454

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“…EDSD was introduced to circumvent the difficulties encountered in problems exhibiting discontinuous behaviors 2 (structural impact [3][4][5] and nonlinear aeroelasticity 6,7 ). It is also well suited for problems with multiple failure modes.…”

Section: Introductionmentioning

confidence: 99%

“…6 The main idea of the multi-fidelity algorithm referred to as MF-EDSD is to create an adaptive envelope around the low-fidelity boundary that defines the region of the design space in which training samples are classified by the high-fidelity model. Training samples outside this envelope are classified by the low-fidelity model.…”

Section: Introductionmentioning

confidence: 99%

Construction of Aeroelastic Stability Boundaries Using a Multi-Fidelity Approach

Dribusch¹,

Missoum²

2012

53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials ConferenceSelf Cite

4
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Two of the challenges in the construction of aeroelastic stability boundaries are the high cost of simulations and the binary nature (stable/unstable) of the problem. This paper introduces a multi-fidelity approach for the construction of a stability boundary using a Support Vector Machine classifier. The boundary is refined using an adaptive sampling scheme which automatically selects the level of fidelity (low or high) needed for each sample. One of the key features of the approach stems from the iterative definition of the region of the space where high-fidelity samples are needed. The proposed method brings a major improvement to a published work on the topic. 1 The efficiency of the approach is tested on two analytical problems of several dimensions before it is applied to the construction of the stability boundary including both flutter and divergence of a simplified parameterized wing.

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“…The idea is that the samples of model outputs at one design point provide useful information (based on linear correlation) about the samples of model outputs at a different design point.There have been recent efforts to bring multifidelity concepts to various topics of uncertainty quantification. In rare event simulation (such as reliability analysis), an approach that is conceptually similar to multifidelity optimization is to evaluate the low-fidelity model extensively to narrow down the location of the limit-state boundary and correct the estimate using the high-fidelity model [4,5]. Non-intrusive polynomial approximations (e.g., polynomial chaos expansion, stochastic collocation) of the high-fidelity model outputs can be constructed by combining an approximation of the low-fidelity model on a fine sparse grid with an approximation of the correction on a coarse sparse grid [6].…”

mentioning
confidence: 99%

Multifidelity approaches for optimization under uncertainty
Ng
¹
,
Willcox
²

2014
Int. J. Numer. Meth. Engng
178
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133
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SUMMARYIt is important to design robust and reliable systems by accounting for uncertainty and variability in the design process. However, performing optimization in this setting can be computationally expensive, requiring many evaluations of the numerical model to compute statistics of the system performance at every optimization iteration. This paper proposes a multifidelity approach to optimization under uncertainty that makes use of inexpensive, low-fidelity models to provide approximate information about the expensive, high-fidelity model. The multifidelity estimator is developed based on the control variate method to reduce the computational cost of achieving a specified mean square error in the statistic estimate. The method optimally allocates the computational load between the two models based on their relative evaluation cost and the strength of the correlation between them. This paper also develops an information reuse estimator that exploits the autocorrelation structure of the high-fidelity model in the design space to reduce the cost of repeatedly estimating statistics during the course of optimization. Finally, a combined estimator incorporates the features of both the multifidelity estimator and the information reuse estimator. The methods demonstrate 90% computational savings in an acoustic horn robust optimization example and practical design turnaround time in a robust wing optimization problem.

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A multifidelity approach for the construction of explicit decision boundaries: application to aeroelasticity

Cited by 30 publications

References 23 publications

Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization

Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization

Construction of Aeroelastic Stability Boundaries Using a Multi-Fidelity Approach

Multifidelity approaches for optimization under uncertainty

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