  The goal of this paper is to study new cosmological models where the dark
energy is a varying Chaplygin gas. This specific dark energy model with
non-linear EoS had been often discussed in modern cosmology. Contrary to
previous studies, we consider new forms of non-linear non-gravitational
interaction between dark matter and assumed dark energy models. We applied the
phase space analysis allowing understanding the late time behavior of the
models. It allows demonstrating that considered non-gravitational interactions
can solve the cosmological coincidence problem. On the other hand, we applied
Bayesian Machine Learning technique to learn the constraints on the free
parameters. In this way, we gained a better understanding of the models
providing a hint which of them can be ruled out. Moreover, the learning based
on the simulated expansion rate data shows that the models cannot solve the
$H_{0}$ tension problem.
