Stochastic Simulators Based Optimization by Gaussian Process Metamodels – Application to Maintenance Investments Planning Issues

Browne, Thomas; Iooss, Bertrand; Gratiet, Loïc Le; Lonchampt, Jérôme; Rémy, Emmanuel

doi:10.1002/qre.2028

Cited by 19 publications

(18 citation statements)

References 26 publications

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“…More advanced techniques predict the probability density function (pdf) [47] or the quantile function [48] of the output given an input value. If the output is scalar, then this case can be perceived and approached as the functional output problems described in the previous item.…”

Section: Scope Of the Methodologymentioning

confidence: 99%

Gaussian process metamodeling of functional-input code for coastal flood hazard assessment

Betancourt

Bachoc

Klein

et al. 2020

Reliability Engineering & System Safety

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et al.. Gaussian process metamodeling of functional-input code for coastal flood hazard assessment. Reliability Engineering and System Safety, Elsevier, 2020, 198, Abstract This paper investigates the construction of a metamodel for coastal flooding early warning at the peninsula of Gâvres, France. The code under study is an hydrodynamic model which receives time-varying maritime conditions as inputs. We concentrate on Gaussian pocess metamodels to emulate the behavior of the code. To model the inputs we make a projection of them onto a space of lower dimension. This setting gives rise to a model selection methodology which we use to calibrate four characteristics of our functional-input metamodel: (i) the family of basis functions to project the inputs; (ii) the projection dimension; (iii) the distance to measure similarity between functional input points; and (iv) the set of functional predictors to keep active. The proposed methodology seeks to optimize these parameters for metamodel predictability, at an affordable computational cost. A comparison to a dimensionality reduction approach based on the projection error of the input functions only showed that the latter may lead to unnecessarily large projection dimensions. We also assessed the adaptability of our methodology to changes in the number of training and validation points. The methodology proved its robustness by finding the optimal solution for most of the instances, while being computationally efficient.

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Section: Scope Of the Methodologymentioning

confidence: 99%

Gaussian process metamodeling of functional-input code for coastal flood hazard assessment

Betancourt

Bachoc

Klein

et al. 2020

Reliability Engineering & System Safety

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“…Following [18,19], one straightforward way to build a surrogate model is the Infer-and-Fit algorithm presented in Algorithm 1.…”

Section: Infer-and-fit Algorithmmentioning

confidence: 99%

Replication-based emulation of the response distribution of stochastic simulators using generalized lambda distributions

Zhu,

Sudret

2019

Preprint

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Due to limited computational power, performing uncertainty quantification analyses with complex computational models can be a challenging task. This is exacerbated in the context of stochastic simulators, the response of which to a given set of input parameters, rather than being a deterministic value, is a random variable with unknown probability density function (PDF). Of interest in this paper is the construction of a surrogate that can accurately predict this response PDF for any input parameters. We suggest using a flexible distribution family -the generalized lambda distribution -to approximate the response PDF. The associated distribution parameters are cast as functions of input parameters and represented by sparse polynomial chaos expansions. To build such a surrogate model, we propose an approach based on a local inference of the response PDF at each point of the experimental design based on replicated model evaluations. Two versions of this framework are proposed and compared on analytical examples and case studies.

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“…Metamodeling of stochastic functions is a less mature field. Assum-ing that the model output is a Gaussian field trajectory, recent studies [11,12,13,14] build two independent or joint deterministic metamodels to fit the mean and the covariance of the assumed Gaussian process. Also based on the joint metamodeling approach, [15] simultaneously surrogates the mean and the dispersion using two interlinked Generalized Additive Models.…”

Section: Introductionmentioning

confidence: 99%

Surrogate Modeling of Stochastic Functions-Application to Computational Electromagnetic Dosimetry

Azzi

Huang

Sudret

et al. 2019

Int. J. UncertaintyQuantification

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Metamodeling of complex numerical systems has recently attracted the interest of the mathematical programming community. Despite the progress in high performance computing, simulations remain costly, as a matter of fact, the assessment of the exposure to radio frequency electromagnetic fields is computationally prohibitive since one simulation can require hours. Moreover, in many engineering problems, carrying out deterministic numerical operations without considering uncertainties can lead to unreliable designs. In this paper we focus on the surrogate modeling of a particular type of computational models called stochastic simulators. In contrast to deterministic simulators which yield a unique output for each set of input parameters, stochastic simulators inherently contain some sources of randomness and the output at a given point is a probability density function. Characterizing the stochastic simulators is even more time consuming. This paper represents stochastic simulators as a stochastic process and describes a metamodeling approach based on the Karhunen-Loève spectral decomposition.

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Stochastic Simulators Based Optimization by Gaussian Process Metamodels – Application to Maintenance Investments Planning Issues

Cited by 19 publications

References 26 publications

Gaussian process metamodeling of functional-input code for coastal flood hazard assessment

Gaussian process metamodeling of functional-input code for coastal flood hazard assessment

Replication-based emulation of the response distribution of stochastic simulators using generalized lambda distributions

Surrogate Modeling of Stochastic Functions-Application to Computational Electromagnetic Dosimetry

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