In this study we develop a computational approach to the solution of an inverse modelling problem concerning the material properties of electrolytes used in Lithium-ion batteries. The dependence of the diffusion coefficient and the transference number on the concentration of Lithium ions is reconstructed based on the concentration data obtained from an in-situ NMR imaging experiment. This experiment is modelled by a 1D time-dependent PDE describing the evolution of the concentration of Lithium ions with prescribed initial concentration and fluxes at the boundary. The material properties that appear in this model are reconstructed by solving a variational optimization problem in which the least-square error between the experimental and simulated concentration values is minimized. This optimization problem is solved using an innovative gradient-based method in which the gradients are obtained with adjoint analysis. In the thesis we develop and validate a computational framework for this reconstruction problem. Reconstructed material properties are presented for a lab-manufactured and a commercial battery electrolyte providing insights which complement available experimental results. / Thesis / Master of Science (MSc)