Machine learning and generative AI techniques offer powerful tools for advanced applications in modelling, estimation and control of dynamical systems, and the combination of these data-based approaches with the model-based knowledge typical in such applications is currently the object of much research attention. This allocation will comprise a number of independent projects within this area; one main theme will be the development of efficient and robust generative flow matching (FM) models capable of learning from limited or distributed data while preserving physical consistency and privacy. These models have recently transformed data synthesis and representation learning by offering powerful tools for modelling complex, high-dimensional data distributions. However, in many scientific and engineering applications, data are scarce, noisy, or inherently decentralised, which limits the practicality of existing FM approaches. First, we will incorporate physics-informed constraints into the FM framework, leveraging established physical laws and system dynamics to guide the generative process, in order to enable more effective use of limited data, improve generalisation, and enhance interpretability. Second, we will extend FM to a federated setting, where data remain distributed across multiple clients or institutions that cannot share raw samples due to privacy or ownership restrictions. To make this feasible, we will design algorithms that address key challenges in federated learning, including communication efficiency, privacy protection, and group fairness, enabling collaborative training of high-quality generative models without compromising data security. The other main strand of research is the incorporation of physical and system-theoretical constraints in deep learning architectures. In control problems, we often have access to prior information in the form of physical laws which the systems under study are known to satisfy, as well as more general system-theoretical properties. A number of methods have recently been developed to enforce these types of constraints in learning-based methods, an area generally known as physics-informed machine learning. In our work, we develop new approaches of this type tailored to controlled dynamical systems, and evaluate their performance in challenging estimation and control applications, such as traffic systems and neuromorphic computing.