This paper deals with the application of the support vector machine (SVM) and the leastsquares SVM regressions to the uncertainty quantification of complex systems with a high-dimensional parameter space. The above regression techniques are used to build accurate and compact surrogate models of the system responses from a limited set of training samples. The accuracy and the feasibility of the proposed modeling techniques are then investigated by comparing their results with the ones predicted by a sparse polynomial chaos expansion by considering two real-life problems with 8 and 30 random variables, respectively. INDEX TERMS Machine learning, uncertainty quantification, parameterized modeling, surrogate models, SVM regression, LS-SVM regression, sparse PC expansion, integrated voltage regulator (IVR), wireless power transfer (WPT). I. INTRODUCTION
International audienceThis paper deals with electromagnetic compatibility simulations at early design stage of equipment or systems development. In this context, expensive simulations based on rigorous modeling are performed, including numerous uncertain variables. The most important configurations are those associated to extreme values of the observed quantity. In this paper we introduce a variance reduction technique to accelerate the estimation of an extreme quantile of theoutput distribution. The approach is based on using a simple model (at a low computational cost) to identify relevant realizations of uncertain variables in strata partitioning the output space of the model. Applicationof the method is detailed on a rather simple cable system in order to estimate an extreme quantile level ofan interfering current. We show that extreme current values are obtained at a reduced computational costcompared to a standard empirical quantile estimation
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