Augmented Gaussian Random Field: Theory and Computation
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We provide a rigorous theoretical foundation for incorporating data of observable and its derivatives of any order in a Gaussian-random-field-based surrogate model using tools in real analysis and probability. We demonstrate that under some conditions, the random field representing the derivatives is a Gaussian random field (GRF) given that its structure is derived from the GRF regressing the data of the observable. We propose an augmented Gaussian random field (AGRF) framework to unify these GRFs and calculate the prediction of this surrogate model in a similar manner as the conventional Gaussian process regression method. The advantage of our method is that it can incorporate arbitrary order derivatives and deal with missing data.
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