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Start of funding 01.01.2023

Control and Machine Learning

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Machine Learning (ML) is forging a new era in Applied Mathematics (AM), generating rich, intensive, innovative research, insightful new ideas and powerful methods. However, simultaneously, this is leading to very challenging fundamental, deep and complex mathematical questions since ML needs reliable methods with theoretical guarantees that can explainably assure good performance and generalisation properties. This also has important ethical consequences and implications.

This great challenge can be addressed through connection with other, more mature areas of AM, from multiple perspectives. This project seeks to develop the rich interface between Control Theory (CT) and ML. We also aim to contribute to building the analytical foundations of the theory of ML needed to understand and improve the computational efficiency of some methods in ML, such as those arising in the context of Residual Neural Networks (ResNets) for Supervised Learning (SL) and Federated Learning (FL), which will also significantly enlarge and update the range of applications of CT.

Final report:
The BACATEC project has been an extraordinary opportunity for our team at FAU to strengthen our collaboration with Professor Miroslav Krstic and, more broadly, with the University of California San Diego and the scientific community in California. The project’s main theme, the interface between systems control and machine learning, is currently experiencing remarkable advances, as both techniques converge to address contemporary challenges such as digital twins.

In addition to the collaboration with Professor Krstic, we have expanded our network of partners to other groups, including those of Professors Jorge Cortés and Sonia Martínez (UCSD), Professor Yuhua Zhu (UCLA), Houman Owhadi (Caltech), and Wei Kang (Naval Postgraduate School, Monterey).

This project has also enabled us to broaden our collaborative network in the United States and to attract additional funding sources, both from the European Office of the AFOSR and the Humboldt Foundation, which, for example, made possible the sabbatical visit of Professor Weiwei Hu (University of Atlanta) to FAU.

The results developed within this project have been published in various outlets and contributed to the invitation of E. Zuazua to deliver a lecture at the International Congress of Mathematicians (ICM 2026) in Philadelphia, where the outcomes of the project will be presented, with particular emphasis on the new perspectives they open for a better understanding of generative diffusion processes.