  Jets from supermassive black holes in the centers of active galaxies are the
most powerful persistent sources of electromagnetic radiation in the Universe.
To infer the physical conditions in the otherwise out-of-reach regions of
extragalactic jets we usually rely on fitting of their spectral energy
distribution (SED). The calculation of radiative models for the jet non-thermal
emission usually relies on numerical solvers of coupled partial differential
equations. In this work machine learning is used to tackle the problem of high
computational complexity in order to significantly reduce the SED model
evaluation time, which is needed for SED fitting with Bayesian inference
methods. We compute SEDs based on the synchrotron self-Compton model for blazar
emission using the radiation code ATHE${\nu}$A, and use them to train Neural
Networks exploring whether these can replace the original computational
expensive code. We find that a Neural Network with Gated Recurrent Unit neurons
can effectively replace the ATHE${\nu}$A leptonic code for this application,
while it can be efficiently coupled with MCMC and nested sampling algorithms
for fitting purposes. We demonstrate this through an application to simulated
data sets and with an application to observational data. We offer this tool in
the community through a public repository. We present a proof-of-concept
application of neural networks to blazar science. This is the first step in a
list of future applications involving hadronic processes and even larger
parameter spaces.
