Stochastic Dynamical System

Stochastic dynamical systems model systems evolving over time under the influence of randomness, aiming to predict their behavior and understand the underlying processes. Current research focuses on developing data-driven methods for learning these systems from observations, employing diverse architectures like neural networks (including autoencoders, GANs, and diffusion models), normalizing flows, and reservoir computing, often coupled with techniques from optimal transport and Bayesian inference. These advancements are significant for improving predictions in various fields, from chemical engineering and wildfire prediction to financial modeling and control systems design, by enabling more accurate and robust modeling of inherently uncertain phenomena.