  We develop a neural network based pipeline to estimate masses of galaxy
clusters with a known redshift directly from photon information in X-rays. Our
neural networks are trained using supervised learning on simulations of eROSITA
observations, focusing in this paper on the Final Equatorial Depth Survey
(eFEDS). We use convolutional neural networks which are modified to include
additional information of the cluster, in particular its redshift. In contrast
to existing work, we utilize simulations including background and point sources
to develop a tool which is usable directly on observational eROSITA data for an
extended mass range from group size halos to massive clusters with masses in
between $10^{13}M_\odot<M<10^{15}M_\odot.$ Using this method, we are able to
provide for the first time neural network mass estimation for the observed
eFEDS cluster sample from Spectrum-Roentgen-Gamma/eROSITA observations and we
find consistent performance with weak lensing calibrated masses. In this
measurement, we do not use weak lensing information and we only use previous
cluster mass information which was used to calibrate the cluster properties in
the simulations. When compared to simulated data, we observe a reduced scatter
with respect to luminosity and count-rate based scaling relations.
  We comment on the application for other upcoming eROSITA All-Sky Survey
observations.
