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

将大型数据集无缝集成到复杂的计算模型中，是21世纪数学科学研究的核心挑战之一。当计算模型是基于进化方程的，数据集是时间有序的，将模型和数据结合起来的过程称为“数据同化”。将数据同化到计算模型中服务于广泛的目的，从模型校准和模型比较一直到新模型设计原则的验证。数据同化领域在很大程度上是由气象学、水文学和油藏勘探领域的从业人员推动的。然而，该领域的理论基础在很大程度上是缺失的。此外，许多新的应用正在从生物学、医学和认知神经科学等领域出现。这些领域需要新的数据同化技术。因此，CRC的目标是双重的：1)开发数据同化的原则方法，2)通过在已建立的和新的应用领域实施这些方法来展示这些方法的计算有效性和鲁棒性。虽然目前大多数数据同化算法是从贝叶斯的角度推导和分析的，但CRC从一般统计推断的角度来看待数据同化。主要的挑战来自推理问题的高维性、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.