Learning Dynamical Systems Using Dynamical Systems

Decanato - Facoltà di scienze informatiche

Data: 10 Gennaio 2022 / 11:30 - 13:00

USI Campus EST, room C1.04, Sector C // online on MS Teams

You are cordially invited to attend the PhD Dissertation Defence of Pietro Verzelli on Monday 10 January 2022 at 11:30 in room C1.04 or online on MS Teams.

Title: "Learning Dynamical Systems Using Dynamical Systems"

Dynamical systems have been used to describe a vast range of phenomena, including physical sciences, biology, neurosciences, and economics just to name a few. The development of a mathematical theory for dynamical systems allowed researchers to create precise models of many phenomena, predicting their behaviors with great accuracy. For many challenges of dynamical systems, highly accurate models are notably hard to produce due to the enormous number of variables involved and the complexity of their interactions. Yet, in recent years the availability of large datasets has driven researchers to approach these complex systems with machine learning techniques. These techniques are valuable in settings where no model can be formulated explicitly; not rarely their predictions lack explainability. In this context, this work aims at advancing the field by “opening the black-box” of data-driven models developed for dynamical systems. We focus on Recurrent Neural Networks (RNNs), one of the most promising and yet less understood approaches. In particular, we concentrate on a specific neural architecture that goes under the name of Reservoir Computing (RC). We address three problems: (1) how the learning procedure of these models can be understood and improved, (2) how these systems encode a representation of the inputs they receive, and (3) how the dynamics of these systems affect their performance. We make use of various tools taken from the theory of dynamical systems to explain how we can better understand the working principles of RC in dynamical systems, aiming at developing new guiding principles to improve their design.

Dissertation Committee:
- Prof. Cesare Alippi, Università della Svizzera italiana, Switzerland (Research Advisor)
- Prof. Lorenzo Livi, University of Manitoba, Canada (Research co-Advisor)
- Prof. Rolf Krause, Università della Svizzera italiana, Switzerland (Internal Member)
- Prof. Andrea Emilio Rizzoli, IDSIA, Switzerland (Internal Member)
- Prof. Peter Ashwin, University of Exter, UK (External Member)
- Prof. Alessio Micheli, University of Pisa, Italy (External Member)
- Prof. Juan-Pablo Ortega, NTU, Singapore (External Member)