Seminario (ORARIO ANTICIPATO) - The Pontryagin maximum principle and the training of Runge-Kutta neural networks

il giorno 17 dicembre alle ore 12:00 presso l'aula 3 del DMI, nell'ambito delle attività del CIMAT (Centro Interdipartimentale di Matematica per la Tecnologia "A. M. Anile"), il prof. Alfio Borzì della Università di Würzburg terrà un seminario dal titolo
The Pontryagin maximum principle and the training of Runge-Kutta neural networks

Abstract: In residual neural networks and related NN architectures,  supervised learning problems can be reformulated as optimal control problems governed by discrete-in-time nonlinear evolution models. 

This talk is devoted to the analysis of these problems in  the framework of a discrete version of the Pontryagin maximum principle and of residual neural networks with Runge-Kutta (RK) structure. In particular, a sequential quadratic hamiltonian (SQH) method for solving  the corresponding supervised learning problems is presented. Convergence properties of the SQH scheme are investigated theoretically  and numerically, and results of numerical experiments are presented that successfully validate the SQH learning algorithm.