  In the context of modeling spectral energy distributions (SEDs) for blazars,
we extend the method that uses a convolutional neural network (CNN) to include
external inverse Compton processes. The model assumes that relativistic
electrons within the emitting region can interact and up-scatter external
photon originating from the accretion disk, the broad-line region, and the
torus, to produce the observed high-energy emission. We trained the CNN on a
numerical model that accounts for the injection of electrons, their
self-consistent cooling, and pair creation-annihilation processes, considering
both internal and all external photon fields. Despite the larger number of
parameters compared to the synchrotron self-Compton model and the greater
diversity in spectral shapes, the CNN enables an accurate computation of the
SED for a specified set of parameters. The performance of the CNN is
demonstrated by fitting the SED of two flat-spectrum radio quasars, namely 3C
454.3 and CTA 102, and obtaining their parameter posterior distributions. For
the first source, the available data in the low-energy band allowed us to
constrain the minimum Lorentz factor of the electrons, $\gamma_{\rm min}$,
while for the second source, due to the lack of these data, $\gamma_{\rm min} =
10^2$ was set. We used the obtained parameters to investigate the energetics of
the system. The model developed here, along with one from B\'egu\'e et al.
(2023), enables self-consistent, in-depth modeling of blazar broadband
emissions within leptonic scenario.
