The prediction of Adaptive Optics (AO)-corrected PSFs offers considerable potential, with implications ranging from enhanced observational planning to the post-processing of astronomical data. The intricate nature of AO-corrected PSFs necessitated the development of advanced analytical models capable of efficiently capturing their intricate morphology. In this work, we utilize the TIPTOP[3] PSF model to predict on-axis PSFs produced by the SPHERE instrument of ESO’s UT3. TIPTOP accepts integrated (reduced) telemetry as input. In theory, the physics-based analytical nature of TIPTOP should result in precise PSF predictions when using reduced telemetry as inputs to the PSF model. However, our research underscores a divergence from this expectation. By utilizing real on-sky datasets recorded on SPHERE, we demonstrate that the calibration of these analytical models is essential for improved prediction accuracy. This work introduces an approach to calibrating PSF models by conjoining them with a feed-forward Neural Network (NN). Furthermore, we present two methodologies to approach its training. Our findings reveal that the calibrated PSF model can achieve a prediction error of 13.6% on real on-sky datasets, while on simulated data, PSF prediction error can be further reduced to only 1.7%. Without calibration, the direct application of the PSF model results in errors of 34.6% for on-sky data and 14.8% for synthetic datasets.