Here, we focus on a specific route to overcome the scarce training data bottleneck, namely the generation of random synthetic training data under suitable constraints determined by the physics involved . In our approach we aim at modelling system dynamics by encoding it into a Hamilton matrix for the interaction of (bound) electrons with intense laser light. The latter can be very noisy and fluctuating from shot to shot, as produced by X-ray Free Electron Lasers (XFEL). We vary the elements of the Hamilton matrix randomly about a matrix of an existing model system in one physical dimension (1D), creating synthetic Hamilton matrices (SHMs) for systems which could but do not necessarily exist in nature for which calculations can be done quickly compared to real 3D systems. From the large set of SHMs augmented with different deterministic realizations of noisy laser pulses, we compute photoelectron spectra to train a fully-connected deep neural network (DNN). Figure shows an application of the DNN (trained with spectra from SHMs) to a real 3D system for which it predicts, without knowing the system explicitly, how the noisy spectrum would look like if a "clean" (Gaussian) laser pulse would have been used. The good agreement with the ground truth demonstrates that the trained DNN can be transferred from 1D to 3D problems and gives confidence in our SHM deep learning concept (SHM-DL). Very recently, the idea of synthetic data generation based on existing data has been taken up for composite materials , where a limited number of original full-field micro-mechanical simulation data are randomly rotated in physical 3D space to generate additional data to train a recurrent neural network for the non-linear elasto-plastic response of Short Fiber Reinforced Composites. Similar ideas using TL are being explored in other areas .