Existing and upcoming instrumentation is collecting large amounts of
astrophysical data, which require efficient and fast analysis techniques. We
present a deep neural network architecture to analyze high-resolution stellar
spectra and predict stellar parameters such as effective temperature, surface
gravity, metallicity, and rotational velocity. With this study, we firstly
demonstrate the capability of deep neural networks to precisely recover stellar
parameters from a synthetic training set. Secondly, we analyze the application
of this method to observed spectra and the impact of the synthetic gap (i.e.,
the difference between observed and synthetic spectra) on the estimation of
stellar parameters, their errors, and their precision. Our convolutional
network is trained on synthetic PHOENIX-ACES spectra in different optical and
near-infrared wavelength regions. For each of the four stellar parameters,
Teff, logg, [M/H], and vsini, we constructed a neural
network model to estimate each parameter independently. We then applied this
method to 50 M dwarfs with high-resolution spectra taken with CARMENES (Calar
Alto high-Resolution search for M dwarfs with Exo-earths with Near-infrared and
optical Echelle Spectrographs), which operates in the visible (520-960 nm) and
near-infrared wavelength range (960-1710 nm) simultaneously. Our results are
compared with literature values for these stars. They show mostly good
agreement within the errors, but also exhibit large deviations in some cases,
especially for [M/H], pointing out the importance of a better understanding of
the synthetic gap