The prediction of the occurrence of Solar Energetic Particle (SEP) events has been investigated over many years, and multiple works have presented significant advances in this problem. The accurate and timely prediction of SEPs is of interest to the scientific community as well as mission designers, operators, and industrial partners due to the threat SEPs pose to satellites, spacecrafts, and crewed missions. In this work, we present a methodology for the prediction of SEPs from the soft X-rays of solar flares associated with SEPs that were measured in 1 AU. We use an expansive dataset covering 25 years of solar activity, 1988-2013, which includes thousands of flares and more than two hundred identified and catalogued SEPs. Neural networks are employed as the predictors in the model, providing probabilities for the occurrence or not of a SEP, which are converted to yes/no predictions. The neural networks are designed using current and state-of-the-art tools integrating recent advances in the machine learning field. The results of the methodology are extensively evaluated and validated using all the available data, and it is shown that we achieve very good levels of accuracy with correct SEP occurrence prediction higher than 85% and correct no-SEP predictions higher than 92%. Finally, we discuss further work towards potential improvements and the applicability of our model in real-life conditions.