An adjoint for likelihood maximization

Toal, David J. J.; Forrester, Alexander I. J.; Bressloff, Neil W.; Keane, Andy J.; Holden, Carren M. E.

doi:10.1098/rspa.2009.0096

Cited by 23 publications

(18 citation statements)

References 30 publications

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“…The likelihood gradients can either be calculated analytically or using reverse algorithmic di↵erentiation of the likelihood. The latter is much faster and less dependent on the number of inputs [33]. In this work, the likelihood gradients for the GEK are calculated analytically by estimating the derivative of the concentrated likelihood function with respect to the hyper-parameters as [33],…”

Section: Correlation Functionsmentioning

confidence: 99%

Performance study of gradient-enhanced Kriging

Ulaganathan

Couckuyt

Dhaene

et al. 2015

Engineering with Computers

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The use of surrogate models for approximating computationally expensive simulations has been on the rise for the last two decades. Krigingbased surrogate models are popular for approximating deterministic computer models. In this work, the performance of Kriging is investigated when gradient information is introduced for the approximation of computationally expensive black-box simulations. This approach, known as Gradient Enhanced Kriging, is applied to various benchmark functions of varying dimensionality (2D-20D). As expected, results from the benchmark problems show that additional gradient information can significantly enhance the accuracy of Kriging. Gradient Enhanced Kriging provides a better approximation even when gradient information is only partially available. Further comparison between Gradient Enhanced Kriging and an alternative formulation of Gradient Enhanced Kriging, called indirect Gradient Enhanced Kriging, highlights various advantages of directly employing gradient information, such as improved surrogate model accuracy, better conditioning of the correlation matrix, etc. Finally, Gradient Enhanced Kriging is used to model 6-and 10-variable Fluid-Structure Interaction problems from bio-mechanics to identify the arterial wall's sti↵ness.Keywords Kriging · Surrogate Modelling · Gradient Enhancement · Fluid Structure Interaction S. Ulaganathan · I. Couckuyt · T. Dhaene · E. Laermans Ghent University -iMINDS, Department of Information Technology (INTEC), Gaston Crommenlaan 8, 9050 Ghent, Belgium E-mail: {selvakumar.ulaganathan, ivo.couckuyt, tom.dhaene, eric.laermans}@ugent.be J. Degroote Ghent University, Department of Flow, Heat and Combustion Mechanics, Sint -Pietersnieuwstraat 41, 9000 Ghent, Belgium E-mail: Joris.Degroote@ugent.be 2 S e l v a k u m a r U l a g a n a t h a n e t a l .

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Section: Correlation Functionsmentioning

confidence: 99%

Performance study of gradient-enhanced Kriging

Ulaganathan

Couckuyt

Dhaene

et al. 2015

Engineering with Computers

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“…In this instance both the CPU and GPU implementations of the Kriging functions are developed using Matlab and its inbuilt GPU toolbox. It should also be noted at this point that all of the surrogate modelling and optimization processes presented within this paper, including the GPU acceleration are implemented within the proprietary Rolls-Royce optimization suite OPTIMATv2 [9,19,20,31,32], itself written in Matlab. Figure 12 presents a comparison of the cost associated with the calculation of the log-likelihood function as both the problem dimensionality and the number of sample points, n, increases when the function is evaluated using a desktop CPU operating in single and multi-threaded modes and two different GPUs.…”

Section: Gpu Accelerated Surrogate Model Constructionmentioning

confidence: 99%

“…In the following paper the hybrid particle swarm algorithm of Toal et al [19,20] which utilizes an adjoint of the likelihood function within a local search is employed.…”

Section: Krigingmentioning

confidence: 99%

Isothermal Combustor Prediffuser and Fuel Injector Feed Arm Design Optimization Using the prometheus Design System

Zhang

Toal

Keane

et al. 2015

Journal of Engineering for Gas Turbines and Power

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The prometheus combustor design system aims to reduce the complexity of evaluating combustor designs by automatically defining preprocessing, simulation, and postprocessing tasks based on the automatic identification of combustor features within the computer-aided design (CAD) environment. This system enables best practice to be codified and topological changes to a combustor's design to be more easily considered within an automated design process. The following paper presents the prometheus combustor design system and its application to the multiobjective isothermal optimization of a combustor prediffuser and the multifidelity isothermal optimization of a fuel injector feed arm in combination with a surrogate modeling strategy accelerated via a high-performance graphical processing unit (GPU).

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“…¶ It should be noted that for high dimensional data sets, d > 10, a substantial increase in computational time can occur and techniques by [36] will be required to efficiently circumvent this cost. Further reductions in time can be achieved by keeping the hyperparameter θ c constant over several iterations.…”

Section: Co-krigingmentioning

confidence: 99%

A Multi-Fidelity Based Adaptive Sampling Optimisation Approach for the Rapid Design of Double-Negative Metamaterials

Bradley¹

2013

PIER B

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Abstract-Due to the increasing complexity of metamaterial geometric structures, direct optimisation of these designs using conventional approaches, such as Gradient-based and evolutionary algorithms, are often impractical and limited. This is in part due to the inherently high computational cost associated with running multiple expensive high-fidelity full-wave simulations, commonly required to optimise the constitutive parameters of a single metamaterial particle. In order to alleviate this issue, we propose an efficient optimisation approach which exploits the Co-Kriging methodology, such that we can successfully couple varying levels of discretisation and solver accuracy obtained from a 3d full-wave numerical solver suite. In contrast to other optimisation strategies, we investigate the improvement in efficiency of optimisation through the use of the LOLA-Voronoi, in conjunction with Expected Improvement and the embedding of a trustregion framework within our optimisation algorithm, to accelerate the convergence of Co-Kriging. Finally, the effectiveness of the outlined algorithm will be demonstrated by a quantitative evaluation of the performance of optimised planar 2D negative index of refraction structures.

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An adjoint for likelihood maximization

Cited by 23 publications

References 30 publications

Performance study of gradient-enhanced Kriging

Performance study of gradient-enhanced Kriging

Isothermal Combustor Prediffuser and Fuel Injector Feed Arm Design Optimization Using the prometheus Design System

A Multi-Fidelity Based Adaptive Sampling Optimisation Approach for the Rapid Design of Double-Negative Metamaterials

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