Surrogate modeling based on statistical techniques for multi-fidelity optimization
Rémi Lam · DSpace@MIT (Massachusetts Institute of Technology) · 2014
Designing and optimizing complex systems generally requires the use of numerical models. However, it is often too expensive to evaluate these models at each step of an optimization problem. Instead surrogate models can be used to explore the design space, as they are much cheaper to evaluate. Constructing a surrogate becomes challenging when different numerical models are used to compute the same quantity, but with different levels of fidelity (i.e., dif-ferent levels of uncertainty in the models). In this work, we propose a method based on statistical techniques to build such a multi-fidelity surrogate. We introduce a new definition of fidelity in the form of a variance metric. This variance is characterized by expert opinion and can vary across the design space. Gaussian processes are used to create an intermediate surrogate for each model. The uncertainty of each inter-mediate surrogate is then characterized by a total variance, combining the posterior variance of the Gaussian process and the fidelity variance. Finally, a single multi-fidelity surrogate is constructed by fusing all the intermediate surrogates. One of