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The International Centre for Mathematical Sciences (ICMS)

In the last few years, an important trend has emerged for using data-driven image models, in particular encoded by neural networks. Novel families of hybrid imaging methodologies, mixing data-driven and traditional mathematical approaches (such as optimisation or sampling methods) have flourished. For instance, generative or discriminative networks such as GANS, VAEs or normalising flows, can be either used in optimisation or sampling schemes as data-driven regularisers for solving inverse problems. Similarly, denoising networks or more generally regularising networks can be incorporated into optimisation or sampling schemes leading to Plug-and-Play methods. From another perspective, unrolled optimisation approaches have been investigated to provide robust network architectures as alternative to traditional black-box end-to-end networks. All these approaches have shown a remarkable versatility and efficiency to solve inverse imaging problems.

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The International Centre for Mathematical Sciences (ICMS)

The workshop addresses recent advances in the numerical and theoretical analysis of Hamilton-Jacobi equations and mean-field PDEs, which lie at the heart of optimal control, differential games, and the modelling of large-scale interacting systems. These equations are central to many applications in physics, finance, engineering, and the social sciences, yet their analysis and numerical approximation remain challenging due to their nonlinear, degenerate, and often high-dimensional nature. Attention will be given to the development of robust numerical methods with proven convergence properties, including semi-Lagrangian schemes, finite element and viscosity approaches, and recent techniques based on scientific machine learning. The workshop will explore the interplay between analytical theory and computational practice, aiming to connect Hamilton-Jacobi and mean-field models with related fields such as stochastic control and optimal transport. By bringing together researchers from across numerical analysis, PDE theory, applied analysis and probability, the event seeks to stimulate new collaborations and perspectives on both foundational problems and real-world applications.