Cokriging for multivariate Hilbert space valued random fields: application to multi-fidelity computer code emulation

Grujic, Ognjen; Menafoglio, Alessandra; Yang, Guang; Caers, Jef

doi:10.1007/s00477-017-1486-9

Cited by 13 publications

(5 citation statements)

References 40 publications

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“…Knowing that the AR(1) multifidelity model for GP regression uses cokriging, [26] presents an interesting approach for cokriging in the context of functional outputs, which is based on dimension reduction. An approach to multifidelity with functional outputs is presented in [11] for multivariate Hilbert space valued random fields.…”

Section: Introductionmentioning

confidence: 99%

Multifidelity Surrogate Modeling for Time-Series Outputs

Kerleguer

2023

SIAM/ASA J. Uncertainty Quantification

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This paper considers the surrogate modeling of a complex numerical code in a multifidelity framework when the code output is a time series and two code levels are available: a high-fidelity and expensive code level and a low-fidelity and cheap code level. The goal is to emulate a fast-running approximation of the high-fidelity code level. An original Gaussian process regression method is proposed that uses an experimental design of the low-and high-fidelity code levels. The code output is expanded on a basis built from the experimental design. The first coefficients of the expansion of the code output are processed by a cokriging approach. The last coefficients are processed by a kriging approach with covariance tensorization. The resulting surrogate model provides a predictive mean and a predictive variance of the output of the high-fidelity code level. It is shown to have better performance in terms of prediction errors than standard dimension reduction techniques.

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Section: Introductionmentioning

confidence: 99%

Multifidelity Surrogate Modeling for Time-Series Outputs

Kerleguer

2023

SIAM/ASA J. Uncertainty Quantification

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“…See, e.g., the reviews in [30] and [33]. Many authors have considered generalizations of kriging to functional data: ordinary kriging for functional data is for instance considered in [15,20,34], universal kriging in [9,31,32], kriging with external drift in [24], and cokriging in [21]. Other authors have proposed smoothing methods [1,3,7,29] using roughness penalties that account separately for the regularity of the field in space and in time, in tensor product approaches.…”

Section: Introductionmentioning

confidence: 99%

Modeling spatially dependent functional data via regression with differential regularization

Arnone

Azzimonti

Nobile

et al. 2019

Journal of Multivariate Analysis

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We propose a method for modeling spatially dependent functional data, based on regression with differential regularization. The regularizing term enables to include problem-specific information about the spatio-temporal variation of the phenomenon under study, formalized in terms of a time-dependent partial differential equation. The method is implemented using a discretization based on finite elements in space and finite differences in time. This non-tensor product basis allows to handle efficiently data distributed over complex domains and where the shape of the domain influences the phenomenon's behavior. Moreover, the method can comply with specific conditions at the boundary of the domain of interest. Simulation studies compare the proposed model to available techniques for spatio-temporal data. The method is also illustrated via an application to the study of blood-flow velocity field in a carotid artery affected by atherosclerosis, starting from echo-color doppler and magnetic resonance imaging data.

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“…They also showed that the coarse models generated using global transmissibility upscaling provided accurate rankings of flow responses for a wide range of well configurations. Other multifidelity approaches for UQ have been investigated by Scheidt et al [19] and Grujic et al [12].…”

Section: Introductionmentioning

confidence: 99%

Multifidelity Framework For Uncertainty Quantification With Multiple Quantities Of Interest

2018

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A systematic framework, involving flow simulation and model selection at many fidelity (resolution) levels, is introduced to accurately quantify the impact of geological uncertainty on multiple output quantities of interest (QoIs). The methodology considers large numbers of realizations (O(1000) in the case presented), though very few (O(10)) simulations are performed at the highest resolutions. We proceed from coarser to finer resolution levels, and at each stage simulation results are used to select a subset of realizations to simulate at the next (higher) fidelity level. Models are constructed at all resolution levels through upscaling of the underlying fine-scale realizations. A global transmissibility upscaling procedure is applied for this purpose. Approximate cumulative distribution functions (CDFs) are constructed for all QoIs considered. The QoI values themselves are always computed at the finest scale, but corresponding percentile values are determined using results at a "rank-preserving" (coarser) fidelity level. Detailed results are presented for oil-water flow in a channelized system. Simulations at seven different fidelity levels are used, and eight QoIs are evaluated. Results for the example considered demonstrate accurate reconstruction of fine-scale CDFs for all QoIs, with a speedup factor of about 18 relative to performing all simulations on the fine scale.

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Cokriging for multivariate Hilbert space valued random fields: application to multi-fidelity computer code emulation

Cited by 13 publications

References 40 publications

Multifidelity Surrogate Modeling for Time-Series Outputs

Multifidelity Surrogate Modeling for Time-Series Outputs

Modeling spatially dependent functional data via regression with differential regularization

Multifidelity Framework For Uncertainty Quantification With Multiple Quantities Of Interest

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