Nonlinear Dynamics and Time Series Analysis


Irregular temporal behaviour is ubiquitious in the world surrounding us:
wind speeds, water wave heights, stock market prices, exchange rates,
blood pressure, or heart rate all fluctuate more or less irregularly in time.
Such signals are the output of quite complex systems with nonlinear
feedback loops and external driving. Our goal is to quantify, understand,
model, and predict such irregular fluctuations. Therefore, our research includes the
study of deterministic and stochastic model systems which are selected because
of interesting dynamical/statistical behaviour and which serve as paradigmatic
data models.  We design data analysis methods, we design tests and measures
of performance for such methods, and we apply these to data sets with
various properties. Last but not least, we study data sets because we
wish to understand the underlying phenomena and to improve data based
predictions of fluctuations.

Out of the initially listed examples of data sources, the atmosphere sticks
out for two reasons: On the one hand, the atmosphere is an exciting highly
complex physical system, where many different sub-fields of physics meet:
Hydrodynamical transport, thermodynamics, light-matter interaction, droplett
formation, altogether forming a system which is not only far from equilibrium
but also far from a linear regime around some working point. On the other
hand, climate change and the impact of extreme weather on human civilization
give atmospheric physics a high relevance. Since the only perfect model of the
atmosphere is the real world itself, and since due to very strong nonlinearities
and hierarchical structures the misleading effects of any approximation might
be tremendous, a data based approach to climate issues is urgently needed
as a complement to simulating climate by models.

In a broader context, our work can also seen as part of what nowadays is
called data science: We make huge data sets accessible to our studies, we
design visualization concepts and analysis tools, we test hypothesis,
construct models, and apply forecast schemes similar to machine learning.
The time series aspect enters our work through the fact that  the temporal
order in which data are recorded carries part of the information, and physics
enters as background information, constraints, and reference models.