Adaptive Construction of Multi-fidelity Surrogates Using a Hybrid Classification-Regression Scheme

Surrogates are used in design optimization and uncertainty quantification to approximate costly function evaluations. A discrepancy-based space-decomposing multi-fidelity approach is proposed to build a Gaussian Process (GP)-based surrogate that provides an approximation of a quantity of interest (QoI) over a whole domain. The space decomposition is obtained through clustering and a support vector machine classifier. The surrogates are refined through active learning to select candidate training points in the distinct regions. This selection is based on local and integrated prediction variance information of the GP. This careful selection of points enables the mitigation of the effects of the “curse of dimensionality". This is followed by a model management step that selects the level of fidelity with which to evaluate new points. This is achieved using a probabilistic description of the discrepancy-based space decomposition coupled with local information gain and the cost associated with evaluating each fidelity. The approach is extended to the case where the function predictions are non-deterministic and variance estimates are available through a modification of the co-kriging model to account for aleatoric variance and modified active learning schemes. The proposed deterministic and non-deterministic approaches are applied to analytical test problems with up to five dimensions and three fidelities and an applied vibration problem with two fidelities in three dimensions.