Date: July 13, 2022
Enrique Zuazua, 2022 W.T. and Idalia Reid Prize
Laureate: Prof. Dr. Enrique Zuazua
Affiliation: Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany)
Award: Enrique Zuazua: 2022 W.T. and Idalia Reid Prize
By: SIAM – Society for Industrial and Applied Mathematics
Location: Room “Spirit of Pittsburgh A”. SIAMAN22, SIAM Annual Meeting. Pittsburgh, Pennsylvania (USA)
Born in Eibar “City of Science”, a magical land from Basque Country (Euskadi) in the north of Spain, our Head Prof. Enrique Zuazua will be awarded as 2022 W.T. and Idalia Reid Prize for fundamental theoretical and computational contributions to the Control, Numerics and Analysis of nonlinear PDEs and multi-physical systems with impactful scientific and industrial applications.
Established by Idalia Reid in honor of her husband W. T. Reid and first awarded in 1994, the W. T. and Idalia Reid Prize in Mathematics is awarded annually in the broadly-defined areas of differential equations and control theory.
The prize was presented on July 13th, 2022 by the President at the Prizes and Awards Lunch where Prof. Zuazua talked on “Control and Machine Learning” at the SIAMAN22, SIAM Annual Meeting at the David Lawrence Convention Center, Pittsburgh – Pennsylvania (USA):
Abstract. In this lecture we shall present some recent results on the interplay between Control Theory and Machine Learning, and more precisely, Supervised Learning and Universal 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 Cauchy problem of the ResNet, leading to an ensemble of solutions to be driven 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, 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. It allows deforming half of the phase space while the other 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 ResNet leads to more stable and robust dynamics.
This lecture is inspired in joint work, among others, with Borjan Geshkovski (MIT), Carlos Esteve (Cambridge), Domènec Ruiz-Balet (IC, London) and Dario Pighin (Sherpa.ai).
Congratulations to our Head Prof. Enrique Zuazua!
|| Read the AN22 Prize Spotlight | Enrique Zuazua at SIAM’s website
-Lorenz Biegler (Chair)
-Alina Chertock, North Carolina State University
-Jean-Michel Coron, Université Pierre Et Marie Curie
-Robert Lipton, Louisiana State University
-Helena J. Nussenzveig Lopes, Universidade Federal Do Rio De Janeiro
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