Turnpike control and deep learning

Enrique Zuazua

University of Erlangen-Nuremberg

Thursday 10th December 2020

14:00:00

http://youtu.be/7wCc8mxQlqs

The tunrpike principle, ubiquitous in applications, asserts that in long time horizons optimal control strategies are nearly of a steady state nature. In this lecture we shall survey on some recent results on this topic and present some its consequences on deep supervised learning, and, in particular, in Residual Neural Networks. This lecture will be based in particular on recent joint work with C: Esteve, B. Geshkovski and D. Pighin. Affiliations: [1] Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany [2] Fundación Deusto, Bilbao, Basque Country Spain [3] Universidad Autónoma de Madrid, Spain Contatto: alfio.quarteroni@polimi.it

Enrique Zuazua Iriondo (Eibar, Basque Country - Spain, 1961) dual PhD in Mathematics - University of the Basque Country & Université Pierre et Marie Curie, holds a Chair in Applied Analysis - Alexander von Humboldt Professorship at FAU- Friedrich-Alexander University, Erlangen-Nürnberg (Germany). He leads the research project "DyCon: Dynamic Control", funded by the ERC - European Research Council at Deusto Foundation, University of Deusto - Bilbao (Basque Country, Spain) and the Department of Mathematics, at UAM - Autonomous University of Madrid where he holds secondary appoints as Professor of Applied Mathematics (UAM) and Director of CCM - Chair of Computational Mathematics (Deusto). His fields of expertise in the area of Applied Mathematics cover topics related with Partial Differential Equations, Systems Control and Machine Learning, led to some fruitful collaboration in different industrial sectors such as the optimal shape design in aeronautics and the management of electrical and water distribution networks. With an important high impact on his work (h-index = 41), he has mentored a significant number of postdoctoral researchers and coached a wide network of Science managers. He holds a degree in Mathematics from the University of the Basque Country, and a dual PhD degree from the same university (1987) and the Université Pierre et Marie Curie, Paris (1988). In 1990 he became Professor of Applied Mathematics at the Complutense University of Madrid, to later move to UAM in 2001. He has been awarded the Euskadi (Basque Country) Prize for Science and Technology 2006 and the Spanish National Julio Rey Pastor Prize 2007 in Mathematics and Information and Communication Technology and the Advanced Grants by the European Research Council (ERC) NUMERIWAVES in 2010 and DyCon in 2016. He is an Honorary member of the of Academia Europaea and Jakiunde, the Basque Academy of Sciences, Letters and Humanities, Doctor Honoris Causa from the Université de Lorraine in France and Ambassador of the Friedrisch-Alexandre University in Erlangen-Nurenberg, Germany. He was an invited speaker at ICM2006 in the section on Control and Optimization. From 1999-2002 he was the first Scientific Manager of the Panel for Mathematics within the Spanish National Research Plan and from 2008-2012 he was the Founding Scientific Director of the BCAM - Basque Center for Applied Mathematics. He is also a member of the Scientific Council if a number of international research institutions such as the CERFACS in Toulouse, France and member of the Editorial Board in some of the leading journals in Applied Mathematics and Control Theory