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In this paper, two inhomogeneous single fluid models for the Universe, whichare able to naturally solve the $H_{0}$ tension problem, are discussed. Theanalysis is based on a Bayesian Machine Learning approach that uses agenerative process. The adopted method allows to constrain the free parametersof each model by using the model itself, only. The observable is taken to bethe Hubble parameter, obtained from the generative process. Using the fulladvantages of our method, the models are constrained for two redshift ranges.Namely, first this is done with mock $H(z)$ data over $z\in [0,2.5]$, thuscovering known $H(z)$ observational data, which are most helpful to validatethe fit results. Then, aiming to extend to redshift ranges to be covered by themost recent ongoing and future planned missions, the models are constrained forthe range $z\in[0,5]$, too. Full validation of the results for this extendedredshift range will have to wait for the near future, when higher redshift$H(z)$ data become available. This makes our models fully falsifiable. Finally,our second model here is able to explain the BOSS reported value for $H(z)$ at$z=2.34$.

An analysis of the $H_{0}$ tension problem in a universe with a viscous dark fluid