Generative Bayesian modelling of radio antenna beams. An application to the MeerKAT radio telescope

Accurate primary beam models are essential for high-fidelity calibration and imaging in radio astronomy. Traditional approaches either lack the ability to represent realistic antenna patterns (analytical models) or could become computationally prohibitive to interpolate for wide-bandwidth observations (electromagnetic simulations, direct holographic measurements). We develop a generative beam model that represents both the spatial structure and the frequency variations in the primary beam, while remaining computationally tractable for integration into the calibration and imaging pipelines. We aim to achieve superior accuracy compared to existing parametric models while reducing data storage and computational requirements compared to data-based models. We adopted a non-parametric Bayesian framework grounded in information field theory, implemented using the NIFTy library. The model represents the beam as a base pattern subject to frequency-dependent geometric transformations (scaling and shifting). The Model performance was validated through posterior predictive checks (̧hi^2/ ≈ 1) and compared it against traditional beam models (Gaussian, Airy disc, JimBeam, Eidos, electromagnetic simulation). We applied the new method to holographic data of the array-averaged MeerKAT Stokes I beam in the L band. dof The model achieves 400:1 data compression, while preserving statistical consistency with holographic measurements. It outperforms existing approaches by more than an order of magnitude in mean squared deviation across the MeerKAT L band. The Zernike decomposition of the base beam, combined with frequency-dependent geometric transformations, enables computationally efficient beam reconstruction at an arbitrary spatial resolution. We demonstrate that generative Bayesian modelling provides an accurate, compact, and physically interpretable representation of radio telescope primary beams. The 150 kB per-antenna footprint enables memory slim integration into calibration and imaging software at negligible computational cost. The approach scales favourably to large arrays and wide bandwidths. The methodology can be readily adapted to other radio telescopes, offering a general pathway towards improved calibration precision for current and future radio surveys.