Two-dimensional (2D) materials have received considerable attention as possible electrodes in Li-ion batteries (LIBs), although a deeper understanding of the Li adsorption behavior as well as broad screening of the materials space is still needed. In this work, we build a high-throughput screening scheme that incorporates a learned interaction. First, density functional theory and graph convolution networks are utilized to calculate minimum Li adsorption energies for a small set of 2D metallic materials. The data is then used to find a dependence of the minimum Li adsorption energies on the sum of ionization potential, work function of the 2D metal, and coupling energy between Li+ and substrate. Our results show that variances of elemental properties and density are the most correlated features with coupling. To illustrate the applicability of this approach, the model is employed to show that some fluorides and chromium oxides are potential high-voltage materials with adsorption energies < -7 eV, and the found physics is used as the design principle to enhance the Li adsorption ability of graphene. This physics-driven approach shows higher accuracy and transferability compared with purely data-driven models.