  Interpreting spectropolarimetric observations of the solar atmosphere takes
much longer than the acquiring the data. The most important reason for this is
that the model fitting, or "inversion", used to infer physical quantities from
the observations is extremely slow, because the underlying models are
numerically demanding. We aim to improve the speed of the inference by using a
neural network that relates input polarized spectra to the output physical
parameters. We first select a subset of the data to be interpreted and infer
physical quantities from corresponding spectra using a standard
minimization-based inversion code. Taking these results as reliable and
representative of the whole data set, we train a convolutional neural network
to connect the input polarized spectra to the output physical parameters
(nodes, in context of spectropolarimetric inversion). We then apply the neural
network to the various other data, previously unseen to the network. As a
check, we apply the referent inversion code to the unseen data and compare the
fit quality and the maps of the inferred parameters between the two inversions.
The physical parameters inferred by the neural network show excellent agreement
with the results from the inversion, and are obtained in a factor of $10^5$
less time. Additionally, substituting the results of the neural network back in
the forward model, shows excellent agreement between inferred and original
spectra. The method we present here is very simple for implementation and
extremely fast. It only requires a training data set, which can be obtained by
inverting a representative subset of the observed data. Applying these (and
similar) machine learning techniques will yield orders of magnitude
acceleration in the routine interpretation of spectropolarimetric data.
