[MDS Job Talk] Learning distributions with dynamical systems

Speaker: Nicole Tianjiao Yang (Emory)

Date: 1/14/25

Abstract: Dynamical systems are widely used to model complex real-world phenomena. They are models based on physical principles, which are highly interpretable but have limits in expressive capabilities. Furthermore, the already high dimensional, and complicated behavior make them difficult to analyze and solve. In recent years, data-driven models have excelled at handling high-dimensional data. However, these models face challenges in their interpretability, reliability, robustness, and computational complexity. My vision is to connect stochastic dynamical systems and statistical learning to bridge the gap between physics-based models and data-based models. In this talk, I present some of my work demonstrating the potential in addressing the optimization in dynamical systems and learning problems holistically. I first focus on dynamical systems with interactive and chaotic behaviors. I present my work on decision-making in complex systems through mean-field games and stochastic control. Next, I discuss learning guided by dynamical systems, where the challenges in stochastic generative models are tackled by operator learning and properties in diffusion processes.