Coupling Matrix

Coupling matrices represent the interactions between different components within a system, a crucial concept across diverse scientific fields. Current research focuses on efficiently computing and manipulating these matrices, particularly within optimization problems and data fusion models, employing techniques like low-rank approximations, PARAFAC2-based coupled matrix and tensor factorizations, and Alternating Optimization/Alternating Direction Method of Multipliers algorithms. These advancements improve the accuracy and efficiency of analyses in areas ranging from neural networks solving high-dimensional inverse problems to kinematic modeling of soft robotics and optimization in financial applications. The development of robust and efficient methods for handling coupling matrices is essential for progress in numerous scientific and engineering disciplines.