Challenges in computational and data science

Wil Schilders

Department of Mathematics and Computer Science, TU Eindhoven

For several decades, Computational Science has been recognized as the third discipline alongside the classical disciplines of theory and experimentation.  Virtual design environments are commonplace by now, and used in all branches of industry. A prominent example is the virtual wind tunnel developed by the areospace industry. In recent years, a fourth discipline is emerging, centered around the availability of huge amounts of data, and therefore termed Data Science. Although the discipline so far appears to be claimed by computer scientists, there are many mathematical challenges, some naturally of a statistical nature but also in many other fields of mathematics. Especially interesting is the interlinkage between computational and data sciences, also referred to as data driven science. The main aim remains to extract accurate models of phenomena and processes, but data driven science provides many more opportunities to address challenges that so far seemed unattainable, such as the ‘tiranny of scales’. In this context, model order reduction is also rapidly becoming an indispensable tool. In this presentation, we will discuss the general context, zoom in to a number of specific challenges and methodologies  and give several examples.