Can we learn from matter creation to solve the $H_{0}$ tension problem?

The $H_{0}$ tension problem is studied in the light of a matter creation mechanism (an effective approach to replacing dark energy), the way to define the matter creation rate being of pure phenomenological nature. Bayesian (probabilistic) Machine Learning is used to learn the constraints on the free parameters of the models, with the learning being based on the generated expansion rate, $H(z)$. Taking advantage of the method, the constraints for three redshift ranges are learned. Namely, for the two redshift ranges: $z\in [0,2]$~(cosmic chronometers) and $z\in [0,2.5]$~(cosmic chronometers + BAO), covering already available $H(z)$ data, to validate the learned results; and for a third redshift interval, $z\in[0,5]$, for forecasting purposes. It is learned that the $3\alpha H_{0}$ term in the creation rate provides options that have the potential to solve the $H_{0}$ tension problem.