The DFG SPP 1276 'MetStröm' covers the expertise of Meteorology, Fluid Dynamics, and Applied Mathematics to develop model- as well as grid-adaptive numerical simulation concepts in multidisciplinary projects. The goal of our part of this interdisciplinary research programm is the development and analysis of new data-based stochastic models for describing the low-scale phenomena in turbulent flows and meteorological data observations.
Hence, new methods for clustering time series, that allow a simultaneous dimension reduction of the observed multiscale phenomena and a hidden state identification have to be evolved. Here, a cutting-edge PDE-approach involving FEM-based clustering algorithms, represents a promissing technique, that delivers the desired features and will be implemented and analysed in future research. Watch the video here
Recent developments in time series analysis led to advanced techniques in clustering theory. These algorithms can be used to get additional information out of a financial time series which could be incorporated in modern portfolio theory. Another aspect of the research project is given by the search for robust optimization methods for investment.
Research Projekt "Advanced Methods of Time Series Analysis and their Application to Climate Research and Insurance Risk Optimization" in CSS
The project is aimed at development and application of data-analysis techniques and advanced climate/weather models in the field of climate change research and insurance risk minimization. Meteorological data are multidimensional, nonlinear, and non-stationary. The extension of existing and development of new methods of time series analysis is required to deal with such data (e.g. understand and forecast the underlying trend). Climate change is expected to entail a rise of extreme rare events with catastrophic consequences. The prediction of such events is essential for the minimization of the risk insurance. Keyword at this point is Large Deviation Theory
Research Project "Conformation Dynamics Algorithms" in DFG-Center MATHEON
This is a joint project with the Biocomputing Group. The aim of the project is to develop novel mathematical models and associated efficient and reliable algorithms for computing the dynamics of biomolecular conformations.