In this work, a deep-learning surrogate model is developed with the objective to predict the characteristic modes of any general geometry. Namely, a physics-based correlation function is introduced capable of classifying the modal currents of different geometries. These currents are used in turn to train our image-based supervised deep neural network. To generate the desired number of arbitrary geometrical shapes, Gielis' supershape formula is utilized. As a proof-of-concept, our algorithm is tested on patch antennas that have shapes of perturbed rectangles. Our results show that our deep neural network has good predictive ability.