We applied machine learning to the entire data history of ESO's High Accuracy Radial Velocity Planet Searcher (HARPS) instrument. Our primary goal was to recover the physical properties of the observed objects, with a secondary emphasis on simulating spectra. We systematically investigated the impact of various factors on the accuracy and fidelity of the results, including the use of simulated data, the effect of varying amounts of real training data, network architectures, and learning paradigms. Our approach integrates supervised and unsupervised learning techniques within autoencoder frameworks. Our methodology leverages an existing simulation model that utilizes a library of existing stellar spectra in which the emerging flux is computed from first principles rooted in physics and a HARPS instrument model to generate simulated spectra comparable to observational data. We trained standard and variational autoencoders on HARPS data to predict spectral parameters and generate spectra. Our models excel at predicting spectral parameters and compressing real spectra, and they achieved a mean prediction error of approximately 50 K for effective temperatures, making them relevant for most astrophysical applications. Furthermore, the models predict metallicity ([M/H]) and surface gravity (log g) with an accuracy of approximately 0.03 dex and 0.04 dex, respectively, underscoring their broad applicability in astrophysical research. The models' computational efficiency, with processing times of 779.6 ms on CPU and 3.97 ms on GPU, makes them valuable for high-throughput applications like massive spectroscopic surveys and large archival studies. By achieving accuracy comparable to classical methods with significantly reduced computation time, our methodology enhances the scope and efficiency of spectroscopic analysis.