Mission of DAEDALUS
Due to the massive complexity of physical and engineering systems, traditional modeling based on differential equations (DE-based modeling) today is often no longer capable of providing sufficiently adequate mathematical models, for instance for simulations. One particularly promising way to address this challenge is the incorporation of data measured from the real-world system into the model. One key question in this process, which is still wide open, is the optimal balance between data-adaptiveness in the sense of infusing information from a measured data set into the modeling process and more traditional DE-based modeling. Evidently, this question can only be satisfactorily answered by a combined viewpoint from both the mathematical side and the application side. Consequently, our RTG team is highly interdisciplinary and includes computer scientists, engineers, mathematicians, and physicists. We will focus on two main areas:
- Life sciences, which typically rely heavily on real-world data, and
- fluid dynamics, where traditionally DE-based modeling plays a major role
The mission of our Research Training Group is three-fold: First, the cohort will be trained in the necessary mathematical techniques such as data assimilation, machine learning, mathematical modeling, model reduction, sparse/low-rank methods, and uncertainty quantification. This will be achieved by an `Introductory Intensive Course Period’, advanced training components, and annual winter schools. Second, each PhD student will learn to communicate and collaborate in an interdisciplinary team. This training will begin in the `Interdisciplinary Welcome Week’, and continue with the interdisciplinary PI team heading each project and special events such as research retreats. Third, the range of projects will provide a multitude of viewpoints on the interplay between incorporation of data and DE-based modeling, thereby contributing to developing a deep understanding of the optimal balance between data and models and attacking the challenge of the optimal degree of data-adaptiveness in the modeling process from different angles. The research experience of the PhD students will be rounded off by international interaction and various activities in the rich Berlin scientific landscape. Consequently, our RTG will educate a new generation of interdisciplinary researchers who are highly trained in data science as well as more traditional mathematical modeling and simulation.