In relation to the challenge

The Action Challenge provides a big challenge to the community of researchers interested – with different perspectives and tools – to investigate a multitude of aspects of model order reduction, and further develop methods and theory that is so important for practical applications in industry and science. It is in view of this long plan for the future to join the efforts, to spread knowledge, to increase the impact of the research conducted by single groups. In recent years, researchers are meeting each other more frequently than before, at workshops and at mini-symposia organized at conferences, all with the main theme of model reduction, but often distinct from workshops on related areas like reduced basis methods and tensor analysis that are vital for the new developments in the area of model reduction. By joining the Action, the community will grow into a large collaborative effort, thereby significantly increasing the chances of meeting the Action Challenge. This can already be observed in recent workshops, where advanced problems from the aerospace and automotive industry have been presented and solved using a combination of model order techniques developed in different groups.

The COST Action is particularly suited to inject fuel into this recently established, fast growing international collaboration. It will allow building a community around science and technology topics in the area of model reduction that has previously failed to gather the necessary critical mass. This is absolutely necessary in order to be successful in addressing the Action Challenge. In many domains of science and technology, problems are becoming so complex with corresponding data sets becoming so large that only combined efforts in developing combinations of model reduction with tensor algorithms, reduced basis methods and algorithms from discrete mathematics or other disciplines like data science can lead to the desired reduction of simulation times for realistic simulations. There is a high necessity for error estimations in reduced models, further building of techniques for data-driven reduction, incorporation of stochastic effects, and many more. All of this cannot be overseen by individual groups, and also for national projects it is far too much to be handled. What is needed is a coordinated effort, combining the expertise of all groups, so that the Action Challenge can be adequately dealt with.

The benefits for science will be immense: both in terms of a deep fundamental understanding of how to address complex multiphysics problems using sophisticated model reduction methods, and of development of applicative models. Models that the Action plans to develop/validate will be immediately useful e.g. to industrial and scientific challenges. The Action’s contribution will have an immediate impact on these disciplines, and hence on meeting the Action Challenge. The Action will also share raw computational and experimental data with all the scientific community: this will allow for further breakthroughs in the field. For the first time, the European scientific community will possess the capability to combine all expertise in the field of model reduction, thanks to the integration of research results from tens of different European groups. Central websites and repositories will be extremely useful, thereby easing the communication between the various groups, and making challenges from several different domains available to all Action participants.

The Action will address the Action Challenge by gathering experts from across the academic spectrum including scientists from other disciplines as well as some 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 the understanding of model reduction for complex systems and their application to a large variety of challenges from several scientific domains. The network will bring new and innovative science to bear on the Action Challenge outlined in Section A, constructing new and developing further existing model reduction methodologies and providing building blocks for understanding development of models and strategies that deal with simulations of multiphysics systems. 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, as well as the coordination of efforts at a European level.