May, 20-21 2024
Otranto, Aragonese Castle (Piazza Castello, Otranto – LECCE)
In recent years, the development of the Koopman operator theory has seen applications in various fields of research, from fluid dynamics to control theory to pure mathematics, and also to fundamentals of physics. There are also tantalizing connections to training of deep neural networks.
The Workshop will be conducted in an interdisciplinary setting to foster discussions on further developments and investigations on the role that this recently rediscovered object may play in theoretical and data driven research.
The Koopman operator plays a role both in fundamental discussions, such as the relation between quantum and classical mechanics , and in the development of different application that entail a mixture of physics-driven and data-driven modeling. This may lead to the possible extension of mathematical treatment to phenomena and areas that are not amenable to mathematical description right now, because we are missing the fundamental relation that we think are at the base of their behavior . Examples can be found in social and economic studies, but also in biology, and in other fields, that traditionally have not been investigated using explicit mathematical tools.
The emerging relation between the Koopman operator theory, and artificial intelligence data driven methods, seems to be pointing at the possibility of using the theory as a basis to understand the training and performance of deep learning algorithms. This relation is revealing a profound connection between Koopman operator theory and deep learning algorithms.
Progress is being made in applications of Koopman operator theory to atmospheric, climate, and ocean dynamics. With the recent advances of using machine learning methods in forecasting, interpretability of Koopman operator-based techniques is particularly attractive to reconcile physics-driven and data-driven methodologies.
Agenda
DAY1-May20th
9:00 Welcome, Antonio Navarra and Igor Mezic
Morning Session
9:30 – 10:45 Koopman Theory for Dynamical Systems and Control
– Mezic I. – The Operator is the Model
– Mauroy A. –A brief journey into stability analysis via the Koopman operator
– Susuki Y. – Koopman resolvents of nonlinear dynamical systems
10:45 – 11:00 Discussion
11:00 – 11:30 Coffee Break
11:30 – 12:20 Koopman Theory for Control
– Vaidya U. – Spectral Koopman-based approach for analysis and synthesis of control dynamical system
– Straesser R. – Koopman-based feedback design with stability guarantees
12:20 – 13:00 Discussion
13:00 – 14:00 Lunch Break
Afternoon Session
14:00 – 14:50 Approximations of the Koopman Operator
– Klus S. – Dynamical systems and complex networks: A Koopman operator perspective
– Slipantchuk J. – Spectral convergence results for EDMD applied to expanding maps
14:50 – 15:00 Discussion
15:00 – 15:15 Coffee Break
15:15 – 16:00 Approximations of the Koopman Operator
– Bevanda P. –Koopman Kernels for Learning Dynamical Systems
– Colbrook M. – Can we compute spectral properties of (infinite-dimensional) Koopman operators?
16:00 – 16:15 Discussion
16:15 – 16:30 Break
16:30 – 17:15 General Discussion on state of knowledge on Koopman theory and estimation methods.
17:15 – 19:00 Networking and informal discussions
End of Workshop – Day 1 and Social Dinner (20:30)
DAY2-May21st
Morning Session
9:00 – 9:50 Applications of Koopman Operator
– Navarra A. – Transfer operators for climate variability
– Sanchez P. – Koopman operators in GC
9:50 – 10:05 Discussion
10:05 – 10:25 Coffee Break
10:25 – 11:40 Applications of Koopman Operator Theory
– Kamenar E. – Koopman Meets Soft Robots
– Monfared Z. – Constructing large sets of Koopman operator eigenfunctions
– Malek-Madani R. – Navy
11:40 – 12:00 Discussion: Theory and Approximations of Koopman Operator in Application
12:00 – 13:00 Over all Discussion: Where Do We Stand, and Where Are We Going? What is the way forward?
Speakers: Navarra A., Mezic I.
13:00 – 13:15 Closing Speech by the Mayor of Otranto Francesco Bruni
13:15 – 14:00 Lunch and close
End of workshop
20:30 – Social Dinner
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ORGANIZED BY
Fondazione CMCC