We derive and verify a new type of low-complexity neural networks using the recently introduced spatial singularity expansion method (S-SEM). The neural network consists of a single layer (shallow learning approach to machine learning) but with its activation function replaced by specialized S-SEM radiation mode functions derived by electromagnetic theory. The proposed neural network can be trained by measured near-or far-field data, e.g., RCS, probe-measured fields, array manifold samples, in order to reproduce the unknown source current on the radiating structure. We apply the method to wire structures and show that the various spatial resonances of the radiating current can be very efficiently predicted by the S-SEM-based neural network. Convergence results are compared with Genetic Algorithms and are found to be considerably superior in speed and accuracy.