Machine learning deals with creating algorithms capable of learning from the provided data. These systems have a wide range of applications and can also be a valuable tool for scientific research, which in recent years has been focused on finding new diagnostic techniques for particle accelerator beams. In this context, SPARC_LAB is a facility located at the Frascati National Laboratories of INFN, where the progress of beam diagnostics is one of the main developments of the entire project. With this in mind, we aim to present the design of two neural networks aimed at predicting the spot size of the electron beam of the plasma-based accelerator at SPARC_LAB, which powers an undulator for the generation of an X-ray free electron laser (XFEL). Data-driven algorithms use two different data preprocessing techniques, namely an autoencoder neural network and PCA. With both approaches, the predicted measurements can be obtained with an acceptable margin of error and most importantly without activating the accelerator, thus saving time, even compared to a simulator that can produce the same result but much more slowly. The goal is to lay the groundwork for creating a digital twin of linac and conducting virtualized diagnostics using an innovative approach.