The study of complex systems incorporates various approaches, including dynamical systems theory and machine learning. Dynamical systems theory, established in the 19th century by figures such as Poincaré and Lyapunov, focuses on understanding the qualitative behavior of systems through models. These models, typically expressed through Ordinary/Partial, Underdetermined (Control), Deterministic/Stochastic differential, or difference equations, approximate observed realities. They provide a mathematical framework for analyzing complex systems, although developing precise models for certain challenging domains like climate dynamics, brain function, biological systems, and financial markets is exceptionally challenging.
On the other hand, machine learning focuses on creating algorithms that perform specific tasks, enhancing their performance with increasing data input. Its applications cover a wide range, including computer vision, stock market analysis, speech recognition, recommender systems, and social media sentiment analysis. Machine learning is particularly crucial in scenarios lacking explicit models but rich in measurement data, a frequent situation in contemporary systems. The rise of data-driven technologies is becoming increasingly important across various fields.
The interface between the theory of dynamical systems and machine learning is a relatively unexplored but promising area. This symposium aims to explore this interface, uniting experts from both domains to advance our understanding in two key areas:
Machine Learning for Dynamical Systems: This approach emphasizes analyzing dynamical systems based on observed data, shifting from traditional analytical methods to a data-centric perspective while maintaining mathematical rigor.
Dynamical Systems for Machine Learning: Here, the objective is to apply the principles and tools of dynamical systems theory to examine and enhance machine learning algorithms.
This initiative marks a significant step in integrating the mathematical insights of the theory of dynamical systems with the practical capabilities of machine learning, fostering advancements in both disciplines.
Also, check the Fields Institute website here for more information.
The schedule is provided below.
