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Inverse problems appear in multiple industrial applications. Solving such inverse problems require the repeated solution of the forward problem. This is the most time-consuming stage when employing inversion techniques, and it constitutes a severe limitation when the inversion needs to be performed in real-time. In here, we focus on the real-time inversion of resistivity measurements for geosteering. We investigate the use of a deep neural network (DNN) to approximate the forward function arising from Maxwell's equations, which govern the electromagnetic wave propagation through a media. By doing so, the evaluation of the forward problems is performed offline, allowing for the online real-time evaluation (inversion) of the DNN.

A Deep Neural Network as Surrogate Model for Forward Simulation of Borehole Resistivity Measurements