Carbon materials possess active sites and functionalities on the surface that can attract prominent interest as solid adsorbents for diverse gas adsorption. This study aimed to predict the optimized methane uptake, adsorption energy (E_ad), and adsorbent rediscovery through multitechniques of neural, regression, classifier ML-DFT, and Uniform Manifold Approximation and Projection (UMAP). Nitrogen and oxygen (N/O) functionalities and graphene, graphene oxide (GO), and N-doped GO were applied to the methane storage medium. Multi-ML algorithms were employed for the adsorption energy of CH₄ uptake on (i) N/O functionalities such as pyridinic (N-py), carboxyl (O-II), oxidized (N-x), hydroxyl (O-h), Nitroso (N-ni), and Amine (primary, secondary, and tertiary). (ii) The graphene surfaces are decorated with N/O heteroatoms to construct graphene oxide (GO) and N-doped GO. The DFT calculations were applied by PW91 and the Dmol³ package. N/O-functionalities in the distance of ∼2.0 to 3.1 Å groups obtained E_ad of approximately −2.0 to −4 eV. Further, ML models accomplished the forthcoming rediscovery of CH₄ physisorption by using the multiadsorptive features of optimized adsorbents with an R² of 0.99. ML-derived sensitivity analysis approach was applied to specifications such as deformation adsorption energy, N/O functionality type, and optimized structure. CH₄ adsorption specifications indicate sensitivity levels of −0.03 to 0.02 eV. The synergetic DFT/ML approaches distinguished the modeled and rediscovered phases of CH₄ adsorption on N/O functional groups and graphene structures. UMAP is employed as a new adsorbent screening approach to play a complementary role in the ML modeling process.