This paper demonstrates the application of correlated Gaussian process based approximations to optimization where multiple levels of analysis are available, using an extension to the geostatistical method of co-kriging. An exchange algorithm is used to choose which points of the search space to sample within each level of analysis. The derivation of the co-kriging equations is presented in an intuitive manner, along with a new variance estimator to account for varying degrees of computational 'noise' in the multiple levels of analysis. A multi-fidelity wing optimization is used to demonstrate the methodology.
Forrester et al. REF investigated the applications of correlated Gaussian process based approximations to optimization and demonstrated that correlating analyses at multiple levels of fidelity can improve surrogate modelling.
Multi-fidelity optimization via surrogate modelling
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Mathematics