Zu Chongzhi Center Distinguished Lecture

Date and Time (China standard time): Friday, December 2, 10:00-11:00 am

Zoom ID: 918 9386 2336

Passcode: dkumath

Title: Generalized synchronizations with reservoir systems

Speaker: Juan-Pablo Ortega

Bio: Juan-Pablo Ortega received a Ph.D. degree in mathematics from the University of California, Santa Cruz, Santa Cruz, CA, USA, in 1998. He started his academic career working on geometric mechanics. His current interests are at the interface between geometry, dynamics, and machine learning. After a postdoc at the Ecole Polytechnique Fédérale de Lausanne (Switzerland) he became a researcher at the Centre Nationale de la Recherche Scientifique (CNRS, France). He is now a Professor in mathematics at Nanyang Technological University, Singapore, where he serves as the Head of the Division of Mathematical Sciences and Associate Chair (Faculty) of the School of Physical and Mathematical Sciences. He is also a Foreign Member of the Royal Academy of Sciences of Spain.

Abstract: In this talk, we show that the celebrated Embedding Theorem of Takens is a particular case of a much more general statement according to which, randomly generated linear state-space representations of generic observations of an invertible dynamical system carry in their wake an embedding of the phase space dynamics into the chosen Euclidean state space. This embedding coincides with a natural generalized synchronization that arises in this setup and that yields a topological conjugacy between the state-space dynamics driven by the generic observations of the dynamical system and the dynamical system itself. This result provides additional tools for the representation, learning, and analysis of chaotic attractors and sheds additional light on the reservoir computing phenomenon that appears in the context of recurrent neural networks. This work is a collaboration with Lyudmila Grigoryeva (St. Gallen) and Allen Hart (Bath).