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Gaussian process emulators for computer experiments with inequality constraints: Gaussian process emulators with inequality constraints

Physical phenomena are observed in many fields (sciences and engineering) and are often studied by time-consuming computer codes. These codes are analyzed with statistical models, often called emulators. In many situations, the physical system (computer model output) may be known to satisfy inequali... Full description

Journal Title: Mathematical geosciences 2017, Vol.49 (5), p.557-582
Main Author: Maatouk, Hassan
Other Authors: Bay, Xavier
Format: Electronic Article Electronic Article
Language: English
Subjects:
Publisher: Springer Verlag
ID: ISSN: 1874-8961
Link: https://hal.archives-ouvertes.fr/hal-01096751
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recordid: cdi_hal_primary_oai_HAL_hal_01096751v3
title: Gaussian process emulators for computer experiments with inequality constraints: Gaussian process emulators with inequality constraints
format: Article
creator:
  • Maatouk, Hassan
  • Bay, Xavier
subjects:
  • design
  • dimensional approximation
  • finite
  • Gaussian process emulator
  • inequality constraints
  • modeling of computer experiments AMS subject classifications 60G15
  • Statistics
  • uncertainty quantification
ispartof: Mathematical geosciences, 2017, Vol.49 (5), p.557-582
description: Physical phenomena are observed in many fields (sciences and engineering) and are often studied by time-consuming computer codes. These codes are analyzed with statistical models, often called emulators. In many situations, the physical system (computer model output) may be known to satisfy inequality constraints with respect to some or all input variables. Our aim is to build a model capable of incorporating both data interpolation and inequality constraints into a Gaussian process emulator. By using a functional decomposition, we propose to approximate the original Gaussian process by a finite-dimensional Gaussian process such that all conditional simulations satisfy the inequality constraints in the whole domain. The mean, mode (maximum a posteriori) and prediction intervals (uncertainty quantification) of the conditional Gaussian process are calculated. To investigate the performance of the proposed model, some conditional simulations with inequality constraints such as boundary, monotonicity or convexity conditions are given.
language: eng
source:
identifier: ISSN: 1874-8961
fulltext: no_fulltext
issn:
  • 1874-8961
  • 1874-8953
url: Link


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descriptionPhysical phenomena are observed in many fields (sciences and engineering) and are often studied by time-consuming computer codes. These codes are analyzed with statistical models, often called emulators. In many situations, the physical system (computer model output) may be known to satisfy inequality constraints with respect to some or all input variables. Our aim is to build a model capable of incorporating both data interpolation and inequality constraints into a Gaussian process emulator. By using a functional decomposition, we propose to approximate the original Gaussian process by a finite-dimensional Gaussian process such that all conditional simulations satisfy the inequality constraints in the whole domain. The mean, mode (maximum a posteriori) and prediction intervals (uncertainty quantification) of the conditional Gaussian process are calculated. To investigate the performance of the proposed model, some conditional simulations with inequality constraints such as boundary, monotonicity or convexity conditions are given.
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abstractPhysical phenomena are observed in many fields (sciences and engineering) and are often studied by time-consuming computer codes. These codes are analyzed with statistical models, often called emulators. In many situations, the physical system (computer model output) may be known to satisfy inequality constraints with respect to some or all input variables. Our aim is to build a model capable of incorporating both data interpolation and inequality constraints into a Gaussian process emulator. By using a functional decomposition, we propose to approximate the original Gaussian process by a finite-dimensional Gaussian process such that all conditional simulations satisfy the inequality constraints in the whole domain. The mean, mode (maximum a posteriori) and prediction intervals (uncertainty quantification) of the conditional Gaussian process are calculated. To investigate the performance of the proposed model, some conditional simulations with inequality constraints such as boundary, monotonicity or convexity conditions are given.
pubSpringer Verlag
doi10.1007/s11004-017-9673-2
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