GRK 2433: Differential Equation- and Data-driven Models in Life Sciences and Fluid Dynamics (DAEDALUS)

由于物理和工程系统的巨大复杂性，基于微分方程的传统建模（基于DE的建模）今天通常不再能够提供足够充分的数学模型，例如用于仿真。解决这一挑战的一个特别有希望的方法是将从现实世界系统中测量的数据纳入模型。这个过程中的一个关键问题，这仍然是开放的，是数据自适应性之间的最佳平衡，在这个意义上注入信息从测量数据集到建模过程和更传统的基于DE的建模。显然，这个问题只能从数学方面和应用方面的综合观点得到满意的回答。因此，我们的RTG团队是高度跨学科的，包括计算机科学家，工程师，数学家和物理学家。我们将专注于两个主要领域：（1）生命科学，通常严重依赖于真实世界的数据，以及（2）流体动力学，传统的基于DE的建模起着重要作用。我们的RTG的使命有三个方面：首先，队列将接受必要的数学技术培训，如数据同化，机器学习，数学建模，模型简化，稀疏/低秩方法和不确定性量化。这将通过“入门强化课程”、高级培训部分和年度冬季学校来实现。其次，每个博士生将学习在跨学科团队中进行沟通和合作。该培训将在“跨学科欢迎周”开始开始，并继续与跨学科PI团队领导每个项目和特殊活动，如研究务虚会。第三，项目范围将提供关于数据整合和基于DE的建模之间相互作用的多种观点，从而有助于深入理解数据和模型之间的最佳平衡，并从不同角度应对建模过程中数据适应性的最佳程度的挑战。博士生的研究经验将通过国际互动和丰富的柏林科学景观中的各种活动来完成。因此，我们的RTG将教育新一代的跨学科研究人员，他们在数据科学以及更传统的数学建模和仿真方面训练有素。

Due to the massive complexity of physical and engineering systems, traditional modeling based on differential equations (DE-based modeling) today is often no longer capable of providing sufficiently adequate mathematical models, for instance for simulations. One particularly promising way to address this challenge is the incorporation of data measured from the real-world system into the model. One key question in this process, which is still wide open, is the optimal balance between data-adaptiveness in the sense of infusing information from a measured data set into the modeling process and more traditional DE-based modeling. Evidently, this question can only be satisfactorily answered by a combined viewpoint from both the mathematical side and the application side. Consequently, our RTG team is highly interdisciplinary and includes computer scientists, engineers, mathematicians, and physicists. We will focus on two main areas: (1) Life sciences, which typically rely heavily on real-world data, and (2) fluid dynamics, where traditionally DE-based modeling plays a major role. The mission of our RTG is three-fold: First, the cohort will be trained in the necessary mathematical techniques such as data assimilation, machine learning, mathematical modeling, model reduction, sparse/low-rank methods, and uncertainty quantification. This will be achieved by an ‘Introductory Intensive Course Period’, advanced training components, and annual winter schools. Second, each PhD student will learn to communicate and collaborate in an interdisciplinary team. This training will begin in the ‘Interdisciplinary Welcome Week’, and continue with the interdisciplinary PI team heading each project and special events such as research retreats. Third, the range of projects will provide a multitude of viewpoints on the interplay between incorporation of data and DE-based modeling, thereby contributing to developing a deep understanding of the optimal balance between data and models and attacking the challenge of the optimal degree of data-adaptiveness in the modeling process from different angles. The research experience of the PhD students will be rounded off by international interaction and various activities in the rich Berlin scientific landscape. Consequently, our RTG will educate a new generation of interdisciplinary researchers who are highly trained in data science as well as more traditional mathematical modeling and simulation.