Enrique Zuazua Iriondo
Chair of Dynamics, Control and Numerics – Alexander von Humboldt Professorship at FAU- Friedrich–Alexander University, Erlangen–Nürnberg (Germany), and secondary appointments at Universidad Autónoma de Madrid and the University of Deusto in Bilbao, Spain.
We present some recent results on the interplay between control and Machine Learning.
We adopt the perspective of the simultaneous or ensemble control of systems of Residual Neural Networks (ResNets) and present a genuinely nonlinear and constructive method, allowing to show that such an ambitious goal can be achieved, estimating the complexity of the control strategies.
This property is rarely fulfilled by the classical dynamical systems in Mechanics and the very nonlinear nature of the activation function governing the ResNet dynamics plays a determinant role.
The turnpike property is also analyzed in this context.
This lecture is inspired in joint work, among others, with Borjan Geshkovski (MIT), Carlos Esteve (Cambridge), Domènec Ruiz-Balet (IC, London), Dario Pighin (Sherpa.ai) and Martin Hernández (FAU).
Enrique Zuazua Iriondo (Basque Country – Spain, 1961) holds the Chair of Dynamics, Control and Numerics – Alexander von Humboldt Professorship at FAU- Friedrich–Alexander University, Erlangen–Nürnberg (Germany), and secondary appointments at Universidad Autónoma de Madrid and the University of Deusto in Bilbao, Spain.
His research in Applied Mathematics covers topics in Partial Differential Equations, Systems Control, Numerical Analysis and Machine Learning.
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).
He has been awarded the Euskadi (Basque Country) Prize for Science and Technology 2006, the Spanish National Julio Rey Pastor Prize 2007, the Advanced Grants NUMERIWAVES in 2010 and DyCon in 2016 of the European Research Council (ERC) and the SIAM W.T. and Idalia Reid Prize 2022.
He is an honorary member of the of Academia Europaea and 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.