There are several freely available toolboxes for modeling the sound pressure field of ultrasound transducers and transducer arrays (e.g., Field II, k-Wave, and DREAM, etc.). These model the beam patterns, or how the ultrasound pulse changes depending on where we observe it, i.e., they model the spatial impulse response of the transducers. Normally, the transmitted pulse is not modeled using these toolboxes, but instead it is assumed that this pulse shape is known. Also, the models are based on assumption of an ideal behavior of the transducers, which is not necessarily the case for a real-world transducers. As a consequence, fitting these models to real measurement data, in order for them to mimic the individual transducer available in the lab, is not generally not possible with any numerical accuracy. In this paper we show, instead, how a deep learning approach can be adopted to train a model that with numerical accuracy models an transducer individual. We compare the proposed technique with real measurements and models using the Field II toolbox and show that for the actual transducer at hand, the deep learning approach outperforms the results from Field II.