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
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Pathiraja, S., Reich, S., Stannat, W. (2020): McKean-Vlasov SDEs in nonlinear filtering. arXiv 2007.12658
Maoutsa, D., Reich, S., and Opper, M. (2020). Interacting particle solutions of Fokker-Planck equations through gradient-log-density estimation. Entropy, Vol. 22, 0802. doi:10.3390/e22080802. arXiv:2006.00702
Gottwald, G., and Reich, S. (2020). Supervised learning from noisy observations: Combining machine-learning techniques with data assimilation.arXiv:2007.07383