One of the questions arising as regards to structured materials is how one can compute their cluster concentrations. Specifically, we are interested in deriving the concentrations of the micro-structures in the NMC (Nickel-Manganese-Cobalt) layer of the cathodes of Li-ion batteries. A simulated annealing approach has been used lately for detecting the structure of the whole lattice which is computationally heavy. Here we propose a mathematical model, called cluster approximation model, in the form of a dynamical system for describing the concentrations of different clusters inside the lattice. However, the dynamical system is hierarchical which requires to be truncated. Truncation of the hierarchical system is performed by the nearest-neighbor closure scheme. Also, a novel framework is proposed for an optimal closure of the dynamical system in order to enhance the accuracy of the model. The parameters of the model are reconstructed by the least square approach as a constrained optimization problem by minimizing the mismatch between the experimental data and the model outputs. The model is validated based on the experimental data on a known Li-ion battery cathode and different approximation schemes are compared. The results clearly show that the proposed approach significantly outperforms the conventional method. / Thesis / Master of Science (MSc)