In short, we aim at
methodological developments for the modeling and simulation of complex processes involving cascades of scales derived from prototypical challenges in the natural sciences
Complex systems research is a leading trend in interdisciplinary science today. With multiscale analysis, modeling, and simulation receiving rapidly increasing attention, it has led to a range of innovative modeling concepts and mathematical results. Due to the multitude of contributing disciplines and the complexity of the considered systems, however, there is now a diversity of perspectives, algorithms, and simulation techniques that is difficult to evaluate, compare, and systematize. Exascale computing, while undoubtedly providing unprecedented opportunities, falls short of providing satisfying answers to many questions of multiscale complex systems research because (i) highly detailed model results are almost as hard to understand as their natural counterparts, (ii) even with Moore’s law extrapolated over decades computers will not be able to resolve all details of many systems of interest, and (iii) detailed resolution simulations often yield an excess of data with redundant information overshadowing the essential aspects of the considered system. Hence, multiscale modeling techniques will have to be invoked for the foreseeable future in representing unresolved scales in simulations.
Despite immense progress in recent years, multiscale modeling is still facing fundamental challenges while increasing aspirations appear to widen the gap between what can be done and what is desired. In particular, most existing concepts are designed to handle only two separated scales, while complex systems, e.g., from geophysics or biology, often exhibit a broad range of spatiotemporal scales that originate from interactions of their constituting processes and structures. Such cascades of scales may be composed of discrete steps, induced by corresponding specific processes, and continuous parts resulting from process interactions that are not tied to separable, specific scales. Different steps in such a cascade of scales may or may not feature different effective types of degrees of freedom and governing principles, but in the cases of interest here the overall system behavior is generally the result of across-scale process interactions.
The long-term scientific goals for this CRC are to join mathematical analysis, scientific computing, and the natural sciences to (i) lay solid foundations for the mathematical characterization of such complex multiscale systems and for casting related appliedscience questions into well-defined mathematical problems, and to (ii) develop sound and efficient analytical and computational modeling techniques for their solution. These developments will be driven and guided by concrete application problems from biology, chemistry, physics, and the geo-sciences on which we aim to make sizeable progress in the individual projects.