Control of multi-particle systems, mean-field limits, and applications to deep learning

(Steuerung von Mehrteilchensystemen, Mean-Field Limits und Anwendungen für Deep Learning)

Project Nº: 530756074
Affiliated Entities: Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU, Germany), Catholic University of Korea (CUK, South Korea)
Supported by DFG (Deutsche Forschungsgemeinschaft/ German Research Foundation) and NRF. Südkorea-NRF-DFG-2023 programme
Duration: 2023 – 2024

More than ever before, our society relies on the correct interaction of a large number of individual elements. These could be internet servers, providers and users in an energy grid, or even ‘artificial neurons’ used in deep learning. Such groups of interacting individuals can have a very complex collective behaviour. It is thus difficult to predict and control them. Moreover, classical analysis techniques will soon be unable to handle the increasingly large size of interacting communities encountered in applications. This collaborative research program seeks to deliver fresh ideas to study large interacting communities, including neural networks from deep learning. Our approach will combine the expertise in collective behaviour of Prof. Ko’s group at the Catholic University of Korea (CUK) with recent advances in control theory and machine learning by Prof. Zuazua’s team at FAU Erlangen-Nürnberg. On the one hand, tools created at FAU have enormous potential to disentangle complex collective behaviour studied at CUK. On the other hand, techniques to analyze collective behaviour developed by the CUK team can help explain why deep neural networks work well. This is a fundamental open question in machine learning. We will explore these synergies through a workshop and accelerate knowledge exchange through mutual research visits.

The proposed international collaboration program will explore an interdisciplinary approach to the analysis of large multi-particle systems, which relies on the cross-fertilization between the PIs’ fields of expertise: control theory and machine learning (Prof. Zuazua) and collective dynamics (Prof. Ko). Indeed,
recent advances in control theory and the ability of machine learning to tackle extremely complex problems provide powerful tools to shed light on large-scale multi-particle systems. On the other hand, classical techniques to study collective dynamics, such as so-called mean-field limits, can potentially be leveraged to explain the behaviour of machine learning frameworks such as very deep neural network—a pressing problem in artificial intelligence.