Abstract
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 H0 tension problem.