Linear Dynamical System

Linear dynamical systems (LDS) model the evolution of systems over time using linear equations, aiming to predict future states and understand underlying dynamics. Current research emphasizes developing robust and efficient algorithms for learning LDS parameters from data, including methods based on spectral analysis, tensor decompositions, and deep learning architectures like recurrent neural networks and Koopman operators. These advancements are crucial for applications ranging from neuroscience (modeling neural activity) to robotics (controlling robot movements) and finance (predicting market trends), improving model accuracy, interpretability, and sample efficiency.