Multi-fidelity Adaptive Global Metamodel of Expensive Computer Simulations

The paper presents a multi-fidelity global metamodel for expensive computer simulations, developed as an essential part of efficient simulation-based design optimization under uncertainty. High- and low-fidelity solvers are managed through a multi-fidelity adaptive sampling procedure. The multi-fidelity approximation is built as the sum of a low-fidelity-trained metamodel and the metamodel of the difference (error) between high- and low-fidelity simulations. The metamodels are based on dynamic stochastic radial basis functions, which provide the prediction along with the associated uncertainty. New training points are placed where the prediction uncertainty is maximum. The prediction uncertainty of both the low-fidelity and the error metamodel is considered for the adaptive refinement of the low- and high-fidelity training set, respectively. The method is demonstrated through three analytical test problems and one simple industrial application in ship hydrodynamics. The fitting error of the multi-fidelity metamodel is used as evaluation metric. The comparison with a high-fidelity-trained metamodel shows the effectiveness of the present method.