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
Lydia Stolpmann, University of Potsdam, Department of Mathematics
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Pidstrigach, J. and Reich, S. (2022). Affine-invariant ensemble transform methods for logistic regression. Foundation of Computational Mathematics, 22, doi:10.10007/s10208-022-09550-2.
Molkenthin, C., Donner, C., Reich, S., Zöller, G., Hainzl, S., Holschneider, M. and Opper, M. (2022): GP-ETAS: Semiparametric Bayesian inference for the spatio-temporal Epidemic Type Aftershock Sequence model. Statistics and Computation, Vol. 32, 29. doi:10.1007/s11222-022-10085-3.
Huang, D.Z., Huang, J., Reich, S., and Stuart, A.M. (2022). Efficient derivative-free Bayesian inference for large-scale inverse problems. arXiv:2204.04386.