Relevance and Timeliness

Improved computational model reduction techniques will help cope with the important industrial and societal challenges that are facing Europe. European businesses compete in a global market where in many regions manufacturing and labour costs are much lower. To be competitive in such an arena Europe must rely on innovation. According to the Organisation for Economic Co-operation and Development 2008 Report “Industrial innovation is increasingly based on the results and techniques of scientific research. That research, in turn, is both underpinned and driven by mathematics.” A 2012 Deloitte report commissioned by the UK Engineering and Physical Sciences Research Council (EPSRC) strongly confirms this, by concluding that up to 16 percent of Gross Value Added can be attributed to results of mathematical research. A stunning example is the
numerical wind tunnel developed by Airbus in France and Germany, costing more than 1 billion Euros in development, but now enabling Airbus to design and test aircraft without using any physical wind tunnels. Virtual design environments in other areas of industry are also under development, and are highly dependent on efficient computational techniques, most prominently in the field of model reduction. These environments should be able to handle increasingly large data sets.

The challenge defined in the foregoing section is valid in several of the domains of science and technology. In the environmental sciences, any real-world simulation such as a weather- or climate prediction requires an objective synthesis between a dynamical model of the atmosphere/ocean and noisy, incomplete and heterogeneous observations of the real atmosphere/ocean. To provide this synthesis is the purpose of variational data assimilation. Data assimilation allows using a mathematical atmosphere/ocean model in order to determine uncertain variables (control variables) such as the initial condition or model parameters (e.g. mixing coefficients) from noisy measurements. From the mathematical point of view one has to deal with a very large-scale optimization problem with PDE constraints governed by the atmosphere- and/or ocean model. The
computational costs for this optimization problem increase considerably within the trend towards high-resolution simulation. To reduce these costs nonlinear model reduction techniques must be developed.

In medical research, data from EEG, MRI, or PET scans amounts to multiple mega-, giga-, or potentially even terabytes, with an associated increase in the time required to execute an individual step in NLME model fitting. Similarly, more complex models such as stochastic and partial differential equations, and Markovian and survival models, will push the limits of the current algorithms and implementations. To be able to face the challenges of the near future with the ever increasing complexity of the data and the associated models, increased performance both at the algorithmic and software/hardware levels are deemed crucial, with parameterised and nonlinear model reduction being one of the best candidates to resolve this challenge.

In the area of physics and material sciences, a systematic comparison between numerical simulations and experiments in order to validate new experimental techniques, mathematical modeling and to uncover a cleaner and more complete picture of the physics of air pollution is highly needed. Model reduction plays an important role in reducing the computation times for the complex turbulent flow simulations.

From the above it should be clear that the topic is not only of considerable interest. It is extremely timely, as the demand is high. The simulation of extremely complex models is a topic with numerous applications in areas of importance, with a high potential for innovations and breakthrough scientific results. The mathematics community is required to cross disciplinary borders, and COST Actions are ideal for facilitating such activity.

This COST Action is not only timely but with its networking tools including working group meetings, Short-Term Scientific Missions (STSMs) and training schools is the most appropriate framework to facilitate progress and enable this novel and emerging subject to truly develop and achieve maximum effectiveness.