Surrogate models and surrogate-based design optimisation

Surrogate modelling refers to statistical and numerical techniques to model the relationship between multiple input variables and an output variable. A surrogate model can be considered as a multidimensional surface fitting of the output variable based on the observed data in multidimensional input space. Generally speaking, a surrogate model (a.k.a. response surface model or metamodel) is used to replace expensive numerical or physical experiments with a computationally cheap and sufficiently accurate model. In engineering, decisions are made on information obtained from various kinds of analyses. One way to get information and increase the knowledge of a problem is to conduct experiments; however, in many cases the cost and complexity of the experiments is so high that only a limited number, if any, of observations is feasible. For example, in aerospace engineering, experiments can be very expensive (e.g. extra-territorial missions) or can take a long time (e.g. high-fidelity simulations). Surrogate models help increase the knowledge gained from the observations and predict performance values which cannot be directly observed. Design optimisation aims at finding the best design solution among various alternatives. This typically requires the evaluation of many design candidates. In many engineering applications design evaluations are computationally expensive and there is a constraint on the optimisation budget which makes the optimisation impracticable. In such cases, surrogate models can be used to predict design performance with a small number of evaluations. However, surrogates are an approximation of the experiment of interest. Thus, a good strategy for surrogate-based design optimisation must take into account the inherent approximation errors. Outline: -Introduction into surrogate models and motivation -Performance measures Surrogates: -Least squares problem -RBF -Gaussian Process Regression (Kriging) -Multi-fidelity Gaussian Process Regression (co-Kriging) Surrogate-based optimisation: -General overview -Bayesian Optimisation (Efficient Global Optimization)