Toal, David J.J., Brooks, Christopher James, Forrester, Alexander I.J. and Keane, A.J.
Applications of algorithmic differentiation within surrogate model generation.
In, Eleventh European Workshop on Automatic Differentiation, Shrivenham, UK,
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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