The topic of this COST Action is model reduction, in a very broad sense. Europe is a centre for model reduction, with many renowned experts in all areas related to ‘model reduction’. Research is carried out at a very high level in these areas, with many young people being attracted and participating in workshops and conferences organized on a world wide scale. Researchers from areas that were not directly associated with model reduction are now realizing the often intimate relations and opportunities, and are also participating in scientific discussions. Vice versa, scientists working in the area of model reduction are very active in contacting other research communities to take advantage of the knowledge available in other disciplines, and apply it for model reduction. There is also a lot of attention for the application of model reduction directly to industrial and societal problems, in many different fields. The beauty of model reduction and mathematics in general, is its ability to abstract from the original application, leading to methods that are generally applicable, also to other domains. For this reason, model reduction is by definition a trans-domain activity, being able to transfer results from one application area to another. Model reduction techniques motivated by electronics problems can immediately be applied to mechanical problems. Methods developed in a domain can be abstracted, generalized, and then applied to challenges from another domain.

The network of scientists involved in the area of model reduction within Europe is large and growing, whereas the contribution from mathematical model reduction is now becoming not only recognized but also endorsed by other disciplines. This COST Action will play a seminal role in facilitating links within the various communities. The Action will gather experts from across the academic spectrum including physicists, engineers as well as experts in the private sector to share state of the art knowledge and experience. In this way the Action will support the building of a world leading community versed in developing methods enabling complex multiphysics simulations and their application to industrial and societal challenges. The network will bring new and innovative science to bear on the challenges outlined above, applying principles of complex systems to the construction of both new methodologies and building blocks for understanding development of complex models. Many of these methods are currently under active discussion and require a flexible approach for further development. This involves networking and intensive discussion between the protagonists and parties involved.