Welcome to the collaborative Research Center TRR 181 ”Energy transfers in Atmosphere and Ocean“
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
Liv Heinecke, University of Potsdam, Department of Mathematics
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de Wiljes, Jana, Reich, Sebastian, Stannat, Wilhelm (2018) Long-Time Stability and Accuracy of the Ensemble Kalman--Bucy Filter for Fully Observed Processes and Small Measurement Noise. SIAM J. Applied Dynamical Systems, Vol. 17 (2), pp. 1152-1181. https://epubs.siam.org/doi/10.1137/17M1119056 (free PDF)
Schütt, Heiko H., Rothkegel, Lars O. M., Trukenbrod, Hans A., Reich, Sebastian, Wichmann, Felix A., Engbert, Ralf (2017) Likelihood-based parameter estimation and comparison of dynamical cognitive models. Psychological Review, Vol 124(4), Jul 2017, 505-524 http://dx.doi.org/10.1037/rev0000068
Gilles Blanchard, Marc Hoffmann, Markus Reiß (2017) Early stopping for statistical inverse problems via truncated SVD estimation. arXiv:1710.07278