Gaussian process (GP) models are today widely used to set-up sequential evaluation strategies of expensive computer codes in the case where the evaluation budget is drastically limited.
For example, if the shape of a car front-rear bumper depends on, say, 3 scalar parameters, one might be interested in the values of the 3 parameters which optimize a performance in car crash test simulation. Since crashing a car (real physical experiment) or simulating the crash numerically is expensive and/or very computer intensive, a reasonable optimum needs to be obtained in very few trials.

 

Mathematically, if the function at hand is called f, a typical question is thus to build a greedy evaluation strategy of f which aims at finding its maximum (optimization problem). Other popular questions exist, like finding the input region where f exceeds a given threshold T (inverse problem).
In this talk, we will present a very popular GP-based sequential evaluation strategy of functions for optimization problems - which is based on the so-called Expected Improvement. We will also talk about parallel strategies, and may - in the discussions - find some common ground with survey theory.