Learning Stocastic Dynamical Systems

Erfan Mirzaei (Ph.D. Student)

Dynamical systems are mathematical models used to describe the evolution of state variables over time. These models, often represented by nonlinear differential equations (ordinary or partial), and possibly stochastic, have wide-ranging applications in science and engineering. This project aims to investigate data-driven methods for analyzing dynamical systems. The methods, which can be based on reproducing kernel Hilbert space or deep neural networks should be efficient and allow for principled analysis. The project can explore both theoretical and applied aspects, drawing upon various mathematical techniques such as mathematical statistics, stochastic processes, empirical processes, numerical analysis, optimization, and optimal transport. Additionally, potential applications in computational chemistry, particularly in the field of molecular dynamics, will also be explored.

Primary Host:	Massimiliano Pontil (Istituto Italiano di Tecnologia & University College London)
Exchange Host:	Karim Lounici (École Polytechnique)
PhD Duration:	01 November 2023 - Ongoing
Exchange Duration:	- Ongoing - Ongoing