In engineering applications, common problems rely on optimization: improving system or structure design, health monitoring with damage assessment and control problems. Modern approaches solve these problems using computer simulations to find the best design among all the possibilities or to find the right damage parameters configuration. High-fidelity simulations, like the finite element in structural design or CFD codes for fluid dynamics, have high computational cost that can be computationally untractable. To accelerate the optimization process two main approaches can be used to reduce the overall execution cost: use a small number of model evaluations and use cheaper, but with reduced accuracy, numerical models.