  We aim to constrain the gas density and temperature distributions as well as
gas masses in several T Tauri protoplanetary disks located in Taurus. We use
the 12CO, 13CO, and C18O (2-1) isotopologue emission observed at 0.9 with the
IRAM NOrthern Extended Millimeter Array (NOEMA) as part of the MPG-IRAM
Observatory Program PRODIGE (PROtostars and DIsks: Global Evolution PIs: P.
Caselli & Th. Henning). Our sample consists of Class II disks with no evidence
of strong radial substructures. We use thesedata to constrain the thermal and
chemical structure of these disks through theoretical models for gas emission.
To fit the combined optically thick and thin CO line data in Fourier space, we
developed the DiskCheF code, which includes the parameterized disk physical
structure, machine-learning (ML) accelerated chemistry, and the RADMC-3D line
radiative transfer module. A key novelty of DiskCheF is the fast and feasible
ML-based chemistry trained on the extended grid of the disk physical-chemical
models precomputed with the ANDES2 code. This ML approach allows complex
chemical kinetics models to be included in a time-consuming disk fitting
without the need to run a chemical code. We present a novel approach to
incorporate chemistry into disk modeling without the need to explicitly
calculate a chemical network every time. Using this new disk modeling tool, we
successfully fit the 12CO, 13CO, and C18O (2-1) data from the CI, CY, DL, DM,
DN, and IQ Tau disks. The combination of optically thin and optically thick CO
lines allows us to simultaneously constrain the disk temperature and mass
distribution, and derive the CO-based gas masses. These values are in
reasonable agreement with the disk dust masses rescaled by a factor of 100 as
well as with other indirect gas measurements.
