This paper is about the cosmological framework of f(R, T) gravity for a flat Friedmann-Lemaitre-Robertson-Walker (FLRW) model of the Universe. It is an approach that combines the f(R, T) function with a mixture of f(R) and f(T), where \(f(R)= R\) ; R the Ricci scalar and the matter term \(f(T)=2\lambda T\) ; T the trace of energy-momentum tensor respectively. The model constraints are deduced by employing Bayesian Statistics and neural network approach with the use of observational Hubble data sets, baryonic acoustic oscillation (BAO) measurements, Pantheon+ compilation of Type Ia supernovae (SNe Ia). An Artificial Neural Networks (ANNs) for parameter estimation using the Hubble data, which trains a fiducial model and obtains the parameter values. A comparison between the results obtained from Bayesian method and ANN has been presented too. Furthermore, we observe that CoLFI is a more efficient method for parameter estimation, particularly for intractable likelihood functions or large cosmological models that need significant resources. Some physical properties of the model are also discussed.
