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In the design phase of an electrical machine, finite element (FE) simulation are commonly used to numerically optimize the performance. The output of the magneto-static FE simulation characterizes the electromagnetic behavior of the electrical machine. It usually includes intermediate measures such as nonlinear iron losses, electromagnetic torque, and flux values at each operating point to compute the key performance indicators (KPIs). We present a data-driven deep learning approach that replaces the computationally heavy FE calculations by a deep neural network (DNN). The DNN is trained by a large volume of stored FE data in a supervised manner. During the learning process, the network response (intermediate measures) is fed as input to a physics-based post-processing to estimate characteristic maps and KPIs. Results indicate that the predictions of intermediate measures and the subsequent computations of KPIs are close to the ground truth for new machine designs. We show that this hybrid approach yields flexibility in the simulation process. Finally, the proposed hybrid approach is quantitatively compared to existing deep neural network-based direct prediction approach of KPIs.