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Abstract 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 the computational time, thereby enabling real-time fitting to multiwavelength data sets. As a demonstration, we used the trained CNN withMultiNestto 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 multimessenger constraints in the analysis. The models will be made publicly available via a web interface at the Markarian Multiwavelength Data Center to facilitate self-consistent modeling of multimessenger data from blazar observations. 

Context.Blazars exhibit strong variability across the entire electromagnetic spectrum, including periods of high-flux states commonly known as flares. The physical mechanisms in blazar jets responsible for flares remain poorly understood to date. Aims.Our aim is to better understand the emission mechanisms during blazar flares using X-ray polarimetry and broadband observations from the archetypical TeV blazar Mrk 421, which can be studied with higher accuracy than other blazars that are dimmer and/or located farther away. Methods.We studied a flaring activity from December 2023 that was characterized from radio to very high-energy (VHE;E > 0.1 TeV) gamma rays with MAGIC,Fermi-LAT,Swift,XMM-Newton, and several optical and radio telescopes. These observations included, for the first time for a gamma-ray flare of a blazar, simultaneous X-ray polarization measurements with IXPE, in addition to optical and radio polarimetry data. We quantify the variability and correlations among the multi-band flux and polarization measurements, and describe the varying broadband emission within a theoretical scenario constrained by the polarization data. Results.We find substantial variability in both X-rays and VHE gamma rays throughout the campaign, with the highest VHE flux above 0.2 TeV occurring during the IXPE observing window, and exceeding twice the flux of the Crab Nebula. However, the VHE and X-ray spectra are on average softer, and the correlation between these two bands is weaker than those reported in the previous flares of Mrk 421. IXPE reveals an X-ray polarization degree significantly higher than that at radio and optical frequencies, similar to previous results for Mrk 421 and other high synchrotron peaked blazars. Differently to past observations, the X-ray polarization angle varies by ∼100° on timescales of days, and the polarization degree changes by more than a factor of 4. The highest X-ray polarization degree, analyzed in 12 h time intervals, reaches 26 ± 2%, around which an X-ray counter-clockwise hysteresis loop is measured withXMM-Newton. It suggests that the X-ray emission comes from particles close to the high-energy cutoff, hence possibly probing an extreme case of the Turbulent Extreme Multi-Zone model for which the chromatic trend in the polarization may be more pronounced than theoretically predicted. We model the broadband emission with a simplified stratified jet model throughout the flare. The polarization measurements imply an electron distribution in the X-ray emitting region with a very high minimum Lorentz factor ($$ \gamma\prime_{\mathrm{min}}\gtrsim10^4 $$), which is expected in electron-ion plasma, as well as a variation of the emitting region size of up to a factor of 3 during the flaring activity. We find no correlation between the fluxes and the evolution of the model parameters, which indicates a stochastic nature of the underlying physical mechanism that likely explains the lack of a tight X-ray/VHE correlation during this flaring activity. Such behavior would be expected in a highly turbulent electron-ion plasma crossing a shock front.