Extensive air showers that develop through the atmosphere emit radio signals that can be measured by ground-based antennas. The resulting time-dependent electric fields contain information about the longitudinal development of the shower.

We present a Bayesian reconstruction framework based on Information Field Theory (IFT) that aims to recover the spatio-temporal structure of the macroscopic current densities responsible for radio emission in an extensive air shower. The method combines a fast, differentiable forward model for radio emission with probabilistic inference to reconstruct high-dimensional current-density fields and approximate their posterior distributions.

We demonstrate this approach on synthetic and Monte Carlo simulated data and discuss its performance, as well as the technical challenges and limitations encountered in this reconstruction framework.