Supplementary Material

We present the computational details, following plots: the MLIP-predicted energy compared with DFT calculated energy, MEP and diffusion energy barriers of Li ions at the graphene monolayer and Cu(111) substrate, phonon band structure of graphene monolayer with the variation of MTP hyperparameters, phonon band structure of graphene monolayer and graphene-Cu heterostructure using DFT and MLIP frameworks, graphene-Cu heterostructure with and without DFT-D3 vdW corrections, phonon lifetime of graphene-Cu heterostructure with and without the addition of isotopic scattering to the BTE solution, EBS and DOS of graphene-Cu heterostructure with and without Li intercalation, interlayer binding energy with interlayer distance in graphene-Cu heterostructure, scattering phase space of graphene monolayer and graphene-Cu heterostructure. Following tables: RMSE values of energy per atom and forces for both the training and test datasets, adsorption energies of Li ions over graphene monolayer, Cu(111) and graphene-Cu heterostructure, variation of thermal conductivity of graphene monolayer with variation of grid, RMSE of energy per atom and force and runtime of graphene monolayer with the variation of MTP hyperparameters. in the Supplementary Material