Phase Space

Phase space, a mathematical representation of a system's state using its position and momentum, is central to understanding and predicting the behavior of complex dynamical systems. Current research focuses on developing novel machine learning models, including neural networks tailored to preserve Hamiltonian dynamics (like Lie-Poisson networks and Hamiltonian Generative Networks), and leveraging phase space reconstruction for improved forecasting in diverse applications such as robotics, power systems, and particle beam dynamics. These advancements enable more accurate and efficient simulations, particularly for high-dimensional systems where traditional methods struggle, leading to improved modeling and control across various scientific and engineering domains.