Since its inception in the 19th century through the efforts of Poincaré and Lyapunov, the theory of dynamical systems addresses the qualitative behaviour of dynamical systems as understood from models. From this perspective, the modeling of dynamical processes in applications requires a detailed understanding of the processes to be analyzed. This deep understanding leads to a model, which is an approximation of the observed reality and is often expressed by a system of Ordinary/Partial, Underdetermined (Control), Deterministic/Stochastic differential or difference equations. While models are very precise for many processes, for some of the most challenging applications of dynamical systems (such as climate dynamics, brain dynamics, biological systems or the financial markets), the development of such models is notably difficult.

On the other hand, the field of machine learning is concerned with algorithms designed to accomplish a certain task, whose performance improves with the input of more data. Applications for machine learning methods include computer vision, stock market analysis, speech recognition, recommender systems and sentiment analysis in social media. The machine learning approach is invaluable in settings where no explicit model is formulated, but measurement data is available. This is frequently the case in many systems of interest, and the development of data-driven technologies is becoming increasingly important in many applications.

The intersection of the fields of dynamical systems and machine learning is largely unexplored, and the goal of this symposium is to bring together researchers from these fields to fill the gap between the theories of dynamical systems and machine learning in the following directions:

• Machine Learning for Dynamical Systems: how to analyze dynamical systems on the basis of observed data rather than attempt to study them analytically.

• Dynamical Systems for Machine Learning: how to analyze algorithms of Machine Learning using tools from the theory of dynamical systems.

Organizers: Boumediene Hamzi (Imperial College London), Weinan E (University of Princeton), Donald Estep (Simon Fraser University and CANSSI), Jeroen Lamb (Imperial College London), Robert MacKay (University of Warwick and The Alan Turing Institute), Predrag Milojkovic (U.S. Office of Naval Research Global), Edward Ott (University of Maryland), Florian Shkurti (University of Toronto)

Registration is free but mandatory and can be made here.

Pre-recorded talks and other details are at http://www.fields.utoronto.ca/activities/20-21/dynamical

Live talks are at http://www.fields.utoronto.ca/activities/20-21/dynamical

Schedule (please regularly update the webpage to get the latest schedule)