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.