A Benchmark of Contemporary Metamodeling Algorithms

Bogoclu, Can; Roos, Dirk

doi:10.7712/100016.2039.7645

“…In order to compare the efficiency of the response surface segmented by the OIM and the surface nonsegmented, three benchmark functions used for this purpose are selected [6]. The regression metamodels applied in this experiment are the SVM which has fast a response and reasonable accuracy, and the KR, also called Gauss Process, very popular for its great accuracy, yet very expensive for larger datasets.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Response Surface Mesh with the Outer Input Method

Duarte¹

2021

Preprint

0

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Artificial intelligence in general and optimization tasks applied to the design of aerospace, space,and automotive structures, rely on response surfaces to forecast the output of functions, and are vital part of these methodologies. Yet they have important limitations, since greater precisions require greater data sets, thus, training or updating larger response surfaces become computationally expensive, sometimes unfeasible. This has been a bottle neck limitation to achieve more promising results, rendering many AI related task with a low efficiency.To solve this challenge, a new methodology created to segment response surfaces is hereby presented. Differently than other similar methodologies, the novel algorithm here presented named outer input method, has a very simple and robust operation. With only one operational parameter, maximum element size, it efficiently generates a near isopopulated mesh for any data set with any type of distribution, such as random, Cartesian, or clustered, for domains with any number of coordinates.Thus, it is possible to simplify the response surfaces by generating an ensemble of response surfaces, here denominated response surface mesh. This study demonstrates how a metamodel denominated Kriging, trained with a large data set, can be simplified with a response surface mesh, significantly reducing its often expensive computation costs> experiments here presented achieved an speed increase up to 180 times, while using a dual core parallel processingcomputer. This methodology can be applied to any metamodel, and metamodel elements can be easily parallelized and updated individually. Thus, its already faster training operation has its speed increased.

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“…In optimization, a metamodel, which is also called a response surface or surrogate model, can be applied to reduce computation costs by dismissing unpromising candidate solutions and suggesting promising alternatives. To evaluate the efficiency of a response surfaces, many benchmark functions were created [6].…”

Section: Related Workmentioning

confidence: 99%

“…In order to compare the efficiency of the response surface segmented by the OIM and the surface non-segmented, three benchmark functions used for this purpose are selected [6]. The regression metamodels applied in this experiment are the SVM which has fast a response and reasonable accuracy, and the KR, also called Gauss Process, very popular for its great accuracy, yet very expensive for larger datasets.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Response Surface Mesh with the Outer Input Method

Duarte¹

2021

Preprint

0

View full text Add to dashboard Cite

Artificial intelligence in general and optimization tasks applied to the design of aerospace, space,and automotive structures, rely on response surfaces to forecast the output of functions, and are vital part of these methodologies. Yet they have important limitations, since greater precisions require greater data sets, thus, training or updating larger response surfaces become computationally expensive, sometimes unfeasible. This has been a bottle neck limitation to achieve more promising results, rendering many AI related task with a low efficiency.To solve this challenge, a new methodology created to segment response surfaces is hereby presented. Differently than other similar methodologies, the novel algorithm here presented named outer input method, has a very simple and robust operation. With only one operational parameter, maximum element size, it efficiently generates a near isopopulated mesh for any data set with any type of distribution, such as random, Cartesian, or clustered, for domains with any number of coordinates.Thus, it is possible to simplify the response surfaces by generating an ensemble of response surfaces, here denominated response surface mesh. This study demonstrates how a metamodel denominated Kriging, trained with a large data set, can be simplified with a response surface mesh, significantly reducing its often expensive computation costs> experiments here presented achieved an speed increase up to 180 times, while using a dual core parallel processingcomputer. This methodology can be applied to any metamodel, and metamodel elements can be easily parallelized and updated individually. Thus, its already faster training operation has its speed increased.

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“…Alternatively or complementarily, the computational effort has been reduced for each sample point, e.g., with surrogate based approaches. In these surrogate methods an approximation (surrogate/response surface) of the original model is built using high-fidelity evaluations of a small training set, followed by MC sampling of the surrogate model [9]. In order to build the surrogate different methods have been employed, e.g., linear regression [10], Gaussian process regression [11], or SC [12].…”

Section: Introductionmentioning

confidence: 99%

Yield Optimization Based on Adaptive Newton-Monte Carlo and Polynomial Surrogates

Fuhrländer

¹

,

Georg

²

,

Schöps

³

2020

Int. J. UncertaintyQuantification

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In this paper we present an algorithm for yield estimation and optimization consisting of Hessian-based optimization methods, an adaptive Monte Carlo (MC) strategy, polynomial surrogates, and several error indicators. Yield estimation is used to quantify the impact of uncertainty in a manufacturing process. Since computational efficiency is one main issue in uncertainty quantification, we propose a hybrid method, where a large part of a MC sample is evaluated with a surrogate model, and only a small subset of the sample is reevaluated with a high-fidelity finite element model. In order to determine this critical fraction of the sample, an adjoint error indicator is used for both the surrogate error and the finite element error. For yield optimization we propose an adaptive Newton-MC method. We reduce computational effort and control the MC error by adaptively increasing the sample size. The proposed method minimizes the impact of uncertainty by optimizing the yield. It allows one to control the finite element error, surrogate error, and MC error. At the same time it is much more efficient than standard MC approaches combined with standard Newton algorithms.

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A Benchmark of Contemporary Metamodeling Algorithms

Cited by 13 publications

References 8 publications

Response Surface Mesh with the Outer Input Method

Response Surface Mesh with the Outer Input Method

Response Surface Mesh with the Outer Input Method

Yield Optimization Based on Adaptive Newton-Monte Carlo and Polynomial Surrogates

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