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DESCRIPTION:ISS Informal Systems Seminar\n\nSpeaker: Enrique Zuazua – Fried
 rich–Alexander University\, Germany \n\n   \n\n\n\nAbstract: In this lectu
 re we shall present some recent results on the interplay between control a
 nd Machine Learning\, and more precisely\, Supervised Learning and Univers
 al Approximation. We adopt the perspective of the simultaneous or ensemble
  control of systems of Residual Neural Networks (ResNets). Roughly\, each 
 item to be classified corresponds to a different initial datum for the Cau
 chy problem of the ResNets\, leading to an ensemble of solutions to be dri
 ven to the corresponding targets\, associated to the labels\, by means of 
 the same control. We present a genuinely nonlinear and constructive method
 \, allowing to show that such an ambitious goal can be achieved\, estimati
 ng the complexity of the control strategies. This property is rarely fulfi
 lled by the classical dynamical systems in Mechanics and the very nonlinea
 r nature of the activation function governing the ResNet dynamics plays a 
 determinant role. It allows deforming half of the phase space while the ot
 her half remains invariant\, a property that classical models in mechanics
  do not fulfill. The turnpike property is also analyzed in this context\, 
 showing that a suitable choice of the cost functional used to train the Re
 sNet leads to more stable and robust dynamics.\n\nThis lecture is inspired
  in joint work\, among others\, with Borjan Geshkovski (MIT)\, Carlos Este
 ve (Cambridge)\, Domènec Ruiz-Balet (IC\, London) and Dario Pighin (Sherpa
 .ai).\n\n\nBiography: Enrique Zuazua Iriondo (Eibar\, Basque Country – Spa
 in\, 1961) holds a Chair of Dynamics\, Control and Numerics – Alexander vo
 n Humboldt Professorship at FAU- Friedrich–Alexander University\, Erlangen
 –Nürnberg (Germany). He also leads the research project “DyCon: Dynamic Co
 ntrol”\, funded by the ERC – European Research Council at the Department o
 f Mathematics\, at UAM – Autonomous University of Madrid and Deusto Founda
 tion\, University of Deusto – Bilbao (Basque Country\, Spain)\, where he h
 olds secondary appointments as Professor of Applied Mathematics (UAM) and 
 Director of CCM – Chair of Computational Mathematics (Deusto). His researc
 h in the area of Applied Mathematics covers topics in Partial Differential
  Equations\, Systems Control\, Numerical Analysis and Machine Learning\, a
 nd led to fruitful collaborations in different industrial sectors such as 
 the optimal shape design in aeronautics\, the management of electrical and
  water distribution networks and the design of recommendation systems. His
  research had a high impact (h-index 44) and 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 Basq
 ue Country\, and a dual PhD degree from the same university (1987) and the
  Université Pierre et Marie Curie\, Paris (1988). In 1990 he became Profes
 sor of Applied Mathematics at the Complutense University of Madrid\, to la
 ter 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 P
 astor Prize 2007 in Mathematics and Information and Communication Technolo
 gy\, the Advanced Grants NUMERIWAVES in 2010 and DyCon in 2016 of the Euro
 pean Research Council (ERC) and the SIAM W.T. and Idalia Reid Prize 2022. 
 He is an Honorary member of the of Academia Europaea and Jakiunde\, the Ba
 sque Academy of Sciences\, Letters and Humanities\, Doctor Honoris Causa f
 rom the Université de Lorraine in France and Ambassador of the Friedrisch-
 Alexandre University in Erlangen-Nurenberg\, Germany. He was an invited sp
 eaker at ICM2006 in the section on Control and Optimization. From 1999-200
 2 he was the first Scientific Manager of the Panel for Mathematics within 
 the Spanish National Research Plan and the Founding Scientific Director of
  the BCAM – Basque Center for Applied Mathematics from 2008-2012. He is al
 so a member of the Scientific Council of a number of international researc
 h institutions such as the INSMI-CNRS and CERFACS in France and member of 
 the Editorial Board in some of the leading journals in Applied Mathematics
  and Control Theory.\n
DTSTART:20221216T190000Z
DTEND:20221216T200000Z
LOCATION:CA\, ZOOM
SUMMARY:Control and Machine Learning 
URL:https://www.mcgill.ca/cim/channels/event/control-and-machine-learning-3
 51648
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