Machine Learning (ML) and Control Theory (CT) are two closely interconnected disciplines with highly attractive research problems. This project aims to encourage the application of CT tools in ML and vice versa, and to explore the great application potential of combining these two rapidly evolving fields. Particular emphasis will be placed on the use of control-theoretic tools for the analysis of deep neural networks, on developing algorithms for efficiently solving parameter-dependent control tasks, and on the development of effective and reliable data-driven control methods.
Extended Project Description
In our research we will use classical and well-known tools (model order reduction techniques, universal approximation theorems, backpropagation, stochastic gradient descent, etc.), as well as recently introduced ones such as: neural ordinary differential equations, residual and physics-informed neural networks (ResNets, PINNs), and deep learning based reduced-order modelling (DL-ROM). An interdisciplinary approach to the problems is ensured by the composition of the working group, which brings together researchers from various fields of mathematics and computer science, and the research will be conducted at the theoretical, numerical and experimental levels.