The transverse field profile of light is being recognized as a resource for classical and quantum communications for which reliable methods of sorting or demultiplexing spatial optical modes are required. Here, we demonstrate, experimentally, state-of-the-art mode demultiplexing of Laguerre-Gaussian beams according to both their orbital angular momentum and radial topological numbers using a flow of two concatenated deep neural networks. The first network serves as a transfer function from experimentally-generated to ideal numerically-generated data, while using a unique "Histogram Weighted Loss" function that solves the problem of images with limited significant information. The second network acts as a spatial-modes classifier. Our method uses only the intensity profile of modes or their superposition, making the phase information redundant.