Graph-theoretical models are natural tools for the description of road networks, circuits, communication networks, and abstract relations between objects, hence algorithmic graph problems appear in a wide range of computer science applications. As most of these problems are computationally hard in their full generality, research in graph algorithms, approximability, and parameterized complexity usually aims at identifying restricted variants and special cases, which are at the same time sufficiently general to be of practical relevance and sufficiently restricted to admit efficient algorithmic solutions. The goal of the project is to put the search for tractable algorithmic graph problems into a systematic and methodological framework: instead of focusing on specific sporadic problems, we intend to obtain a unified algorithmic understanding by mapping the entire complexity landscape of a particular problem domain. Completely classifying the complexity of each and every algorithmic problem appearing in a given formal framework would necessarily reveal every possible algorithmic insight relevant to the formal setting, with the potential of discovering novel algorithmic techniques of practical interest. This approach has been enormously successful in the complexity classifications of Constraint Satisfaction Problems (CSPs), but comparatively very little work has been done in the context of graphs. The systematic investigation of hard algorithmic graph problems deserves the same level of attention as the dichotomy program of CSPs, and graph problems have similarly rich complexity landscapes and unification results waiting to be discovered. The project will demonstrate that such a complete classification is feasible for a wide range of graph problems coming from areas such as finding patterns, routing, and survivable network design, and novel algorithmic results and new levels of algorithmic understanding can be achieved even for classic and well-studied problems.

The Sun is an enigmatic star that produces the most powerful explosive events in our solar system - solar flares and coronal mass ejections. Studying these phenomena can provide a unique opportunity to develop a deeper understanding of fundamental processes on the Sun, and critically, to better forecast space weather. The Active Region Classification and Flare Forecasting (ARCAFF) project will develop a beyond state-of-the-art flare forecasting system utilising end-to-end deep learning (DL) models to significantly improve upon traditional flare forecasting capabilities. ARCAFF will increase the accuracy and timeliness of current operational flare forecast products and create new time series flare forecasts. Furthermore, ARCAFF forecasts will include forecast uncertainties, another major improvement over current systems. The large amount of available space-based solar observations are an ideal candidate for this type of analysis, given DL effectiveness in modelling complex relationships. DL has already been successfully developed and deployed in weather forecasting, financial services, and health care domains, but has not been fully exploited in the solar physics domain. Solar flare forecasts from ARCAFF will be benchmarked against current systems using international community standards, and will demonstrate ARCAFF’s superior forecasting capabilities. The datasets, codes and DNNS developed for ARCAFF will be made openly available to support further research efforts and encourage their re-use. ARCAFF is relevant to the work program as it will exploit currently available data space weather data to train DL models to improve forecast accuracy. DL itself is an innovation enabling technology and analysis of the DL models will improve scientific understanding of solar flares. Through the creation of new forecast products it will develop and mature new concepts for both scientific and monitoring purposes, following the best-practices of meteorological services.