  In this work, we present novel Machine Learning and Differentiable
Programming enhanced calibration techniques used to improve the energy
resolution of the Silicon Drift Detectors (SDDs) of the VIP-2 underground
experiment at the Gran Sasso National Laboratory (LNGS). We achieve for the
first time a Full Width at Half Maximum (FWHM) in VIP-2 below 180 eV at 8 keV,
improving around 10 eV on the previous state-of-the-art. SDDs energy resolution
is a key parameter in the VIP-2 experiment, which is dedicated to searches for
physics beyond the standard quantum theory, targeting Pauli Exclusion Principle
(PEP) violating atomic transitions. Additionally, we show that this method can
correct for potential miscalibrations, requiring less fine-tuning with respect
to standard methods.
