  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.
