A comparison between two de Rham complexes in diffeology

There are two de Rham complexes in diffeology. The original one is due to Souriau and the other singular complex defined by a simplicial differential graded algebra. We compare first cohomology groups of within Čech–de spectral sequence making use factor map which connects complexes. As consequence, it follows that algebra irrational torus $T_\theta$ isomorphic tensor product exterior generated non-trivial flow bundle over $T_\theta$.