Very High-Energy GRB Afterglow Fits with Neural-Network Emulation and Bayesian inference

The very high-energy ($E>100$ GeV) afterglow emission in gamma-ray bursts (GRBs) can be explained by synchrotron self-Compton (SSC). Modeling this emission accurately requires fully numerical codes that solve the time-dependent coupled particle–photon kinetic equations while accounting for Klein–Nishina suppression. However, their substantial computational cost makes them impractical for traditional parameter inference techniques such as Markov Chain Monte Carlo (MCMC) sampling. In this work, we present a highly efficient surrogate model based on artificial neural networks (ANNs) that emulates a one-zone kinetic SSC radiation code. To train our ANN, we use a multi-dimensional model parameter grid that constitutes a sample of 100,800 spectra produced by an infinitely thin spherical blast wave propagating inside a constant density interstellar medium (ISM). The ANN reproduces the numerical spectra well, with the median relative error generally below 2 per cent across the full frequency domain. Using this surrogate framework, we perform Bayesian parameter posterior estimation via MCMC and fit the broadband GRB afterglow observations of GRB 190114C from X-rays to TeV $\gamma$-rays at different epochs. We find an energetic jet with isotropic-equivalent kinetic energy of $E_{\mathrm{k},\mathrm{i}\mathrm{s}\mathrm{o}}\simeq 7.2\times {10}^{54}$ erg moving with a coasting bulk Lorentz factor of $\mathrm{\Gamma }\gtrsim 500$ into an ISM with density $n\simeq 0.1\mathrm{c}{\mathrm{m}}^{-3}$. The deviation of our model light curve from observations on long timescales suggests that an ISM environment is inconsistent and a radially stratified external medium, as pointed out by \citet{Aguilar-Ruiz+26}, is preferred instead.