The seamless integration of large data sets into sophisticated computational models provides one of the central research challenges for the mathematical sciences in the 21st century. When the computational model is based on evolutionary equations and the data set is time-ordered, the process of combining models and data is called data assimilation. The assimilation of data into computational models serves a wide spectrum of purposes ranging from model calibration and model comparison all the way to the validation of novel model design principles.
The field of data assimilation has been largely driven by practitioners from meteorology, hydrology and oil reservoir exploration; but a theoretical foundation of the field is largely missing. Furthermore, many new applications are emerging from, for example, biology, medicine, and the neurosciences, which require novel data assimilation techniques. The goal of the proposed CRC is therefore twofold: First, to develop principled methodologies for data assimilation and, second, to demonstrate computational effectiveness and robustness through their implementation for established and novel data assimilation application areas.
While most current data assimilation algorithms are derived and analyzed from a Bayesian perspective, the CRC will view data assimilation from a general statistical inference perspective. Major challenges arise from the high-dimensionality of the inference problems, nonlinearity of the models and/or non-Gaussian statistics. Targeted application areas include the geoscience as well as emerging fields for data assimilation such as biophysics and cognitive neuroscience.
Prof. Dr. Sebastian Reich, University of Potsdam, Department of Mathematics
Dr. Liv Heinecke, University of Potsdam, Department of Mathematics
Our PIs Ralf Engbert and Sebastian Reich together with Maximilian Rabe and Reinhold Kliegl just published the preprint to a study where they modelled…
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Malem-Shinitski, N., Opper, M., Reich, S., Schwetlick, S., Seelig S. A., and Engbert, R (2020). A Mathematical Model of Exploration and Exploitation in Natural Scene Viewing.arXiv: 2004.04649
Roelly, S. and Zass, A. (2020). Marked Gibbs Point Processes with Unbounded Interaction: An Existence Result. Journal of Statistical Physics 179, 972–996 (2020). Open Access
Schindler, D., Moldenhawer, T., Stange, M., Beta, C., Holschneider, M. and Huisinga, W. (2020). Analysis of protrusion dynamics in amoeboid cell motility by means of regularized contour flows.arXiv: 2005.12678