Learning hidden constraints with gaussian process classifiers in the context optimization context
Résumé
Design optimization of engineering systems generally involves the use of complex numerical models that take as input design variables and environmental variables. The environmental conditions are generally simulated to assess the reliability of the proposed designs. Hence the simulations can become computationally very expensive. Moreover, some input conditions can lead to simulation failures or instabilities, due, for instance, to convergence issues of the numerical scheme of complex partial derivative equations. Most of the time, the set of inputs corresponding to failures is not known a priori and corresponds to a hidden constraint, also called crash constraint in this special case. Since the observation of a simulation failure might be as costly as a feasible simulation, we seek to learn the feasible set of inputs and thus target areas without simulation failure during the optimization process. Therefore, we propose a Gaussian Process Classifiers (GPC) active learning method to learn the feasible domain. The proposed methodology is an adaptation of Stepwise Uncertainty Reduction strategies usually used with Gaussian Process Regression, in the classification setting with GPC models. The performance of this strategy on toy problems and on a wind turbine design application will be presented.
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