  Modeling the multiwavelength spectral energy distributions (SEDs) of blazars
provides key insights into the underlying physical processes responsible for
the emission. While SED modeling with self-consistent models is computationally
demanding, it is essential for a comprehensive understanding of these
astrophysical objects. We introduce a novel, efficient method for modeling the
SEDs of blazars by the mean of a convolutional neural network (CNN). In this
paper, we trained the CNN on a leptonic model that incorporates synchrotron and
inverse Compton emissions, as well as self-consistent electron cooling and pair
creation-annihilation processes. The CNN is capable of reproducing the
radiative signatures of blazars with high accuracy. This approach significantly
reduces computational time, thereby enabling real-time fitting to
multi-wavelength datasets. As a demonstration, we used the trained CNN with
MultiNest to fit the broadband SEDs of Mrk 421 and 1ES 1959+650, successfully
obtaining their parameter posterior distributions. This novel framework for
fitting the SEDs of blazars will be further extended to incorporate more
sophisticated models based on external Compton and hadronic scenarios, allowing
for multi-messenger constraints in the analysis. The models will be made
publicly available via a web interface, the Markarian Multiwavelength
Datacenter, to facilitate self-consistent modeling of multi-messenger data from
blazar observations.
