While the abundances of the final state hadrons in relativistic heavy-ion collisions are rather well described by the thermal particle production, the shape of the transverse momentum, \(p_\textrm{T}\) , distribution below \(p_\textrm{T} \approx 500\) MeV/c, is still poorly understood. We propose a procedure to quantify the model-to-data differences using Bayesian inference techniques, which allows for consistent treatment of the experimental uncertainties and tests the completeness of the available hydrodynamic frameworks. Using relativistic fluid framework FluiduM with PCE coupled to TrENTo initial state and FastReso decays, we analyze \(p_\textrm{T}\) distribution of identified charged hadrons measured in heavy-ion collisions at top RHIC and the LHC energies and identify an excess of pions produced below \(p_\textrm{T} \approx 500\) MeV/c. Our results provide new input for the interpretation of the pion excess as either missing components in the thermal particle yield description or as an evidence for a different particle production mechanism.
