A new four dimensional (4D) ab initio potential energy surface (PES) is generated for the collision of C4(3Σg-) with H2(1Σg), considering both molecules as rigid rotors. A supervised neural network model is created to augment the ab initio PES and to get the missing data points. Furthermore, space fixed expansion of the augmented PES is carried out using a least squares fit over two spherical harmonics terms, resulting in radial coefficients (λ1, λ2, and λ). The centre of symmetry in both C4 and H2 forces λ1 and λ2 to have even values, respectively. Moreover, the rotational states of C4 are only populated by odd levels due to its ground state triplet symmetry and the nuclear spin (I = 0) of 12C. The cross-sections and rate coefficients with para and ortho H2 partners are studied for various odd state transitions, where the rate coefficients of the ortho are 10-20% higher than those of the latter. The de-excitation rates obtained by the para H2 collisions are also compared to those of He and are found to be ∼1.7-2.8 times the He rates, across various order transitions. The simple scaling of He rates using a factor of 1.38 proves insufficient to describe para H2 rates. Therefore, these results show the importance of explicitly studying H2 as an important colliding partner, governing the kinetics of various rotational processes in the interstellar space.