The recent developments in the research area have significantly advanced the computational efficiency and accuracy in tensor decomposition and model reduction techniques. Innovations in tensor algebra and decomposition methods are enabling more robust and efficient solutions to complex problems in materials science and liquid crystals. Notably, the integration of tensor t-product algebra with empirical interpolation methods is providing new avenues for handling tensor-valued data without distorting structural information. Additionally, the application of convolution tensor decomposition in solving the Allen-Cahn equation is demonstrating substantial computational benefits, particularly in high-resolution simulations. Furthermore, advancements in modeling wrinkling phenomena in hyperelastic materials are simplifying computational efforts by introducing modified kinematic relationships. The study of the zero inertia limit in liquid crystal models is also contributing to a deeper understanding and more accurate numerical simulations. These developments collectively push the boundaries of computational methods, offering enhanced capabilities for researchers in various fields.