A new four dimensional (4D) ab initio potential energy surface (PES) is generated for the collision of C₄(³Σ_g⁻) with H₂(¹Σ_g), 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.