CRC 1294/2: Data Assimilation – The Seamless Integration of Data and Models

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. However, a theoretical foundation of the field is largely missing. Furthermore, many new applications are emerging from biology, medicine, and cognitive neuroscience, for example. These fields need novel data assimilation techniques. The goal of the CRC is therefore twofold: 1) to develop principled methodologies for data assimilation, and 2) to demonstrate the computational effectiveness and robustness of these methodologies, by implementing them in established and novel application areas. While most current data assimilation algorithms are derived and analysed from a Bayesian perspective, the CRC views data assimilation from a general statistical inference perspective. Major challenges arise from the high dimensionality of the inference problems, the nonlinearity of the models, or non-Gaussian statistics. Targeted application areas include the geosciences, as well as emerging fields for data assimilation such as biophysics, cognitive neuroscience, and pharmacology.