Classical Cepheids in the Galactic thin disk. I. Abundance gradients via non-local thermodynamic equilibrium spectral analysis

Classical Cepheids (CCs) have long been considered excellent tracers of the chemical evolution of the Milky Way's young disk. We present a homogeneous, non-local thermodynamical equilibrium (NLTE) spectroscopic analysis of 401 Galactic CCs, based on 1,351 high-resolution optical spectra, spanning Galactocentric distances from 4.6 to 29.3 kpc. Using PySME with MARCS atmospheres and state-of-the-art grids of NLTE departure coefficients, we derived the atmospheric parameters and abundances for key species tracing multiple nucleosynthetic channels (O, Na, Mg, Al, Si, S, Ca, Ti, Mn, Fe, and Cu). Our sample is the largest CC NLTE dataset to date and it achieves high internal precision, enabling the robust modelling of present-day thin-disk abundance patterns and radial gradients. We estimate abundance gradients using three analytic prescriptions (linear, logarithmic, bilinear with a break) within a Bayesian, outlier-robust framework. We also applied Gaussian process (GP) regression to capture non-parametric variations. We find that NLTE atmospheric parameters differ systematically from LTE determinations. Moreover, iron and most elemental abundance profiles are better described by non-linear behaviour rather than by single-slope linear models: logarithmic fits generally outperform simple linear models, while bilinear fits yield inconsistent break radii across elements. GP models reveal a consistent outer-disk flattening of X/H for nearly all studied elements. The X/Fe ratios are largely flat with Galactocentric radius, indicating coherent chemical scaling with iron across the thin disk, with modest positive offsets for Na and Al and mild declines for Mn and Cu. Finally, Cepheid kinematics confirm thin-disk orbits for the great majority of the sample. Comparisons with recent literature shows an overall agreement, while also highlighting NLTE-driven differences, especially in outer-disk abundances. These results provide tighter empirical constraints for chemo-dynamical models of the Milky Way and set the stage for future NLTE mapping with upcoming large spectroscopic surveys.