Lie Group

Lie groups, continuous groups of transformations with smooth group operations, are increasingly central to various scientific fields, particularly in addressing problems involving symmetries and geometric structures. Current research focuses on developing efficient algorithms for optimization and integration on Lie groups, often leveraging neural networks and geometric integrators tailored to specific group structures (e.g., SE(3), SO(3)) to improve performance in applications like robotics and machine learning. This work is significant because it provides mathematically rigorous and computationally efficient methods for handling data and models with inherent geometric constraints, leading to improved accuracy and generalization in diverse applications ranging from computer vision to multibody dynamics.