Applications of algorithmic differentiation within surrogate model generation
Applications of algorithmic differentiation within surrogate model generation
The construction of a surrogate model for the purposes of design optimisation often involves some form of sub-optimisation of the surrogate's controlling parameters. The construction of a kriging model, for example, can require a series of O(n^3) factorisations of the correlation matrix when performing the likelihood maximisation. Due to the smooth nature of the likelihood function, gradient information can be used to accelerate the likelihood optimisation when employed within a gradient enhanced global optimisation strategy. To this end a series of adjoints of the likelihood function of a variety of kriging based surrogate models are presented.
An adjoint of the likelihood function derived via algorithmic differentiation is presented for traditional kriging. Recent extensions of this formulation to the likelihood functions for co-kriging and gradient enhanced kriging are also presented. Gradient enhanced kriging may be of particular interest to those wishing to employ derivative information from computational simulations, which itself may be a result of an algorithmic differentiation, within a design optimisation.
Toal, David J.J.
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Brooks, Christopher James
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Forrester, Alexander I.J.
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Keane, A.J.
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9 December 2010
Toal, David J.J.
dc67543d-69d2-4f27-a469-42195fa31a68
Brooks, Christopher James
5c504fef-0360-4b2a-b6c4-d88bbd6e5bac
Forrester, Alexander I.J.
176bf191-3fc2-46b4-80e0-9d9a0cd7a572
Keane, A.J.
26d7fa33-5415-4910-89d8-fb3620413def
Toal, David J.J., Brooks, Christopher James, Forrester, Alexander I.J. and Keane, A.J.
(2010)
Applications of algorithmic differentiation within surrogate model generation.
Eleventh European Workshop on Automatic Differentiation, Shrivenham, United Kingdom.
25 pp
.
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Conference or Workshop Item
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Abstract
The construction of a surrogate model for the purposes of design optimisation often involves some form of sub-optimisation of the surrogate's controlling parameters. The construction of a kriging model, for example, can require a series of O(n^3) factorisations of the correlation matrix when performing the likelihood maximisation. Due to the smooth nature of the likelihood function, gradient information can be used to accelerate the likelihood optimisation when employed within a gradient enhanced global optimisation strategy. To this end a series of adjoints of the likelihood function of a variety of kriging based surrogate models are presented.
An adjoint of the likelihood function derived via algorithmic differentiation is presented for traditional kriging. Recent extensions of this formulation to the likelihood functions for co-kriging and gradient enhanced kriging are also presented. Gradient enhanced kriging may be of particular interest to those wishing to employ derivative information from computational simulations, which itself may be a result of an algorithmic differentiation, within a design optimisation.
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Eleventh_EuroAd_Workshop_-_David_Toal__Chris_Brooks__Alex_Forrester_and_Andy_Keane_-_Applications_of_Algorithmic_Differentiation_within_Surrogate_Model_Generation.pdf
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Published date: 9 December 2010
Venue - Dates:
Eleventh European Workshop on Automatic Differentiation, Shrivenham, United Kingdom, 2010-12-09
Organisations:
Computational Engineering & Design Group
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Local EPrints ID: 198561
URI: http://eprints.soton.ac.uk/id/eprint/198561
PURE UUID: 03e60598-52a9-487b-8ab7-aefba7b51f0c
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Date deposited: 05 Oct 2011 09:05
Last modified: 15 Mar 2024 03:29
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Author:
Christopher James Brooks
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