On Monday February 19, 2024, Prof. Enrique Zuazua will talk on Control and Machine Learning at the DEDS2024, Differential Equations for Data Science 2024, the international conference organized (online) on February 19 – 21, 2024.

Abstract. In this lecture we shall present some recent results on the interplay between control 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 ResNets, 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. This viewpoint opens up interesting perspectives to develop new hybrid mechanics-data driven modelling methodlogies. 

This lecture is inspired in joint work, among others, with Borjan Geshkovski (MIT), Carlos Esteve (Cambridge), Domenec Ruiz-Balet (IC, London) and Dario Pighin (

This conference is mainly devoted to new mathematical aspects on machine learning algorithms, big data analysis, and other topics in data science area, from a viewpoint of differential equations. In recent years, several interesting connections between differential equations and data science have been found and attract attention from researchers of differential equations. In this conference, we will gather such researchers of differential equations who have interest in data science and try to shed new light on mathematical foundations on the topics in machine learning/data science.


Mon. February 19, 2024 at 17:00H


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