2025ApJ...990..222S

Modeling the broadband emission of blazars has become increasingly challenging with the advent of multimessenger observations. Building upon previous successes in applying convolutional neural networks (CNNs) to leptonic emission scenarios, we present an efficient CNN-based approach for modeling blazar emission under proton synchrotron and hybrid lepto-hadronic frameworks. Our CNN is trained on extensive numerical simulations generated by SOPRANO, which span a comprehensive parameter space accounting for the injection and all significant cooling processes of electrons and protons. The trained CNN captures complex interactions involving both primary and secondary particles, effectively reproducing electromagnetic and neutrino emissions. This allows for rapid and thorough exploration of the parameter space characteristic of hadronic and hybrid emission scenarios. The effectiveness of the trained CNN is demonstrated through fitting the spectral energy distributions of two prominent blazars, TXS 0506+059 and PKS 0735+178, both associated with IceCube neutrino detections. The modeling is conducted under assumptions of constant neutrino flux across distinct energy ranges, as well as by adopting a fitting that incorporates the expected neutrino event count through a Poisson likelihood method. The trained CNN is integrated into the Markarian Multiwavelength Data Center (www.mmdc.am), offering a robust tool for the astrophysical community to explore blazar jet physics within a hadronic framework.