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This paper focuses on quantifying the uncertainty in the outputs of numerical simulations produced by uncertain positions of the electrodes placed on patient's scalp. In order to avoid running thousands of simulations, an architecture which combines two different artificial neural networks (ANNs) for uncertainty quantification (UQ) is proposed in this paper. The overall aim of this work is to develop a surrogate model for UQ involving high-dimensional data. The proposed method is demonstrated to be an attractive alternative to conventional UQ methods since it shows considerable advantage in the computational expense and speed.