In this study, a computational approach to the solution of an inverse modeling problem is developed to reconstruct unknown material properties of a Li-ion battery. In-situ MRI measurements performed on a layered graphite electrode during charging are used in comparison with Stefan-Maxwell concentrated electrolyte theory, Butler-Volmer reaction kinetics, and multiphase porous electrode theory to explore the overall accuracy of models for Li transport processes in the active material. In particular, the main research goal here is to determine if the original Cahn-Hilliard formulation for phase-separation can be improved upon through extension to a periodic bilayer model (two-layer Cahn-Hilliard). The original model contains a pair of two stable phases at low and high concentrations that produces the ``shrinking core'' behavior for lithiated graphite. The comparative advantage of the periodic bilayer model stems from the capturing of a third stable phase of intermediate concentration as the average between one concentrated layer and one dilute layer. Calibration is done simultaneously on concentration and cell voltage profiles through multi-objective optimization where the accuracy of a model is assessed based on the quantification of agreement with experimental data. The periodic bilayer model is found to improve upon the least-squares error for fitting of concentration profiles by roughly 20%, while the voltage fittings are too similar to be conclusive. / Thesis / Master of Science (MSc)