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The International Centre for Mathematical Sciences (ICMS)

Set against the backdrop of emerging high-performance computational resources, such as the UK’s forthcoming first exascale supercomputer to be sited in Edinburgh, the workshop will focus on the development of new mathematical and algorithmic methodologies aiming to make the most of the computational power of future computer architectures in materials simulation. The workshop will stimulate research collaborations between researchers from the UK, EU and USA, and will offer the opportunity for mathematicians to learn more about the new challenges and opportunities these computational platforms will bring.

Topics to be discussed will include novel approaches to computational multi-tasking and sampling; optimisation methodologies such as numerical continuation and deflation; coarse-graining and model reduction; and the rigorous mathematical analysis of such methodologies.

Modeling and Simulation,    Condensed Matter Physics and Materials

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.

Numerical Analysis and Computational Mathematics,    Neural Networks and Artificial Intelligence, Machine Learning