Over the last decade, machine learning techniques have been widely used in a variety of applications. They have demonstrated their remarkable capabilities to extract patterns and make predictions from large datasets. New approaches based on these techniques have notably been developed in the context of optimal control, in order to offer better alternatives to the study of certain problems deemed to be complex. On the other hand, although machine learning algorithms are producing extraordinary results, they still require a solid mathematical theory that can be used to analyze and build generic neural networks adapted to each type of problem. Recent work has enabled neural networks to be described as discretized forms of optimal control problems, so that certain essential properties can be analyzed through optimal control theory. The aim of this mini-symposium is then to present, on the one hand, some recent applications of machine learning techniques in optimal control context and, on the other hand, how optimal control theory can help to build and analyze neural networks. More precisely, Mario Sperl (University of Bayreuth) will present how deep neural networks can be employed for a curse-of-dimensionality free approximation of optimal value function. Sergio Rodrigues (Johann Radon Institute for Computational and Applied Mathematics) will introduced an approach based on neural networks for the computation of an optimal feedback control minimizing the quadratic energy cost for semilinear parabolic equations. Olivier Bokanowski (Universit´e Paris Cit´e) will propose new neural network approximations of the differential games strategies in feedback form, for which he will provide error estimates. Finally, Antonio Alvarez Lopez (Universidad Aut´onoma de Madrid) will show how optimal control theory can be used to estimate the number of neurons required for efficient classification.
Mini symposium organizers:
Sofya Maslovskaya (Universität Paderborn)
Boris Wembe (Universität Paderborn)

Session 6. Room A5, Friday 09:00-11:00.
Chair: Sofya Maslovskaya (Universität Paderborn)
Speakers:
Mario Sperl (University of Bayreuth) Neural network-based approximation of optimal value functions: exploring decaying sensitivity
Olivier Bokanowski (Université Paris Cité) Neural network for differential games
Sergio S. Rodrigues (Johann Radon Institute for Computational and Applied Mathematics (RICAM) of the Austrian Academy of Sciences) Stabilization of semilinear parabolic equations: explicit and optimal control based feedbacks.
Antonio Álvarez López (Universidad Autónoma de Madrid) Controllability of neural ODEs for data classification.