Data-calibrated point spread function prediction

Context. Precise knowledge of the point spread function (PSF) underpins many data analysis steps in astronomy, from photometry and astrometry to source de-blending and deconvolution. In adaptive optics (AO) observations, however, the PSF is highly variable with wavelength, field position, and observing conditions, making it difficult to model. Traditional PSF reconstruction (PSF-R) requires full AO telemetry and complex infrastructures, limiting its routine use, especially for tomographic systems. Aims. We present a practical framework for fast, accurate, and data-calibrated PSF modeling that captures the spatial and spectral variability of AO-corrected PSFs without relying on complete AO telemetry. Methods. Our approach builds on a Fourier-based PSF model inspired by astro-TIPTOP. As inputs, our model uses only a compact set of physically meaningful parameters retrievable from the ESO archive. A lightweight neural network corrects these inputs to achieve the best match with real data. It is trained end to end with the PSF model, allowing it to learn any miscalibrations directly from on-sky data. Results. The framework achieves high accuracy on on-sky data. On a test set of MUSE-NFM standard stars, it yields median errors of 13.5% in the Strehl ratio and 10.9% in the core full width at half maximum (FWHM). In crowded MUSE-NFM observations of ω Centauri, the method predicts dozens of off-axis, wavelength-dependent PSFs with a Strehl error of <5% and a FWHM error of 4.6%, enabling source separation without per-star PSF extraction. Conclusions. Our compact, physics-informed, and data-calibrated model delivers accurate, polychromatic, and field-varying PSFs without relying on full AO telemetry. While demonstrated on MUSE-NFM, the method is still transferable to other AO-assisted instruments.