SFB 1294: Data Assimilation – The Seamless Integration of Data and Models

将大数据集无缝地集成到复杂的计算模型中，是21世纪数学科学面临的主要研究挑战之一。当计算模式是基于演化方程并且数据集是按时间顺序的时，模式和数据结合的过程称为数据同化。将数据同化到计算模型中的目的广泛，从模型校准和模型比较一直到验证新的模型设计原则。数据同化领域在很大程度上是由气象学、水文学和油藏勘探的从业者推动的。然而，该领域的理论基础在很大程度上是缺乏的。此外，例如，生物学、医学和认知神经科学正在涌现出许多新的应用。这些领域需要新的数据同化技术。因此，儿童权利委员会的目标有两个：1)制定数据同化的原则性方法；2)通过在现有的和新的应用领域实施这些方法，证明这些方法的计算效率和稳健性。虽然大多数目前的数据同化算法是从贝叶斯的角度得出和分析的，但儿童权利委员会从一般统计推断的角度来看待数据同化。主要挑战来自推理问题的高维、模型的非线性或非高斯统计。目标应用领域包括地球科学，以及新兴的数据同化领域，如生物物理学、认知神经科学和药理学。

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, and2) 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.