Low Dimensional

Low-dimensional modeling aims to simplify complex high-dimensional systems by identifying and representing their essential dynamics in a lower-dimensional space. Current research focuses on developing data-driven methods, such as autoencoders, neural ordinary differential equations (NODEs), and variational autoencoders (VAEs), to learn these reduced representations from high-dimensional data, often incorporating techniques like sparse identification of nonlinear dynamics (SINDy) for model identification and stability analysis. This approach is crucial for improving computational efficiency, enabling better understanding of complex systems across diverse fields like fluid dynamics, neuroscience, and control systems, and facilitating the development of more effective control strategies.