Dynamical System

Dynamical systems theory focuses on understanding the evolution of systems over time, aiming to predict future states and uncover underlying mechanisms. Current research emphasizes developing data-driven models, employing architectures like recurrent neural networks, transformers, and physics-informed neural networks, often coupled with techniques from optimal transport and Koopman operator theory, to learn system dynamics from observational data, even in the presence of noise and incomplete information. This field is crucial for advancing scientific understanding across diverse disciplines, from climate modeling and neuroscience to engineering control systems and materials science, by providing robust and efficient tools for analysis, prediction, and control of complex systems. The development of more accurate and efficient methods for learning and analyzing dynamical systems from limited and noisy data remains a key focus.