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，今天基于微分方程的传统建模(基于DE的建模)往往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测量的数据纳入模型。这一过程中的一个关键问题仍然悬而未决，那就是在将来自测量的数据集的信息注入建模过程的意义上的数据适应性与更传统的基于DE的建模之间的最佳平衡。显然，这个问题只有从数学和应用两个方面结合起来才能令人满意地回答。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。我们将关注两个主要领域：(1)生命科学，它通常严重依赖真实世界的数据；(2)流体动力学，传统上基于DE的建模在其中扮演主要角色。我们的RTG的任务有三个方面：第一，将对这批人进行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/低阶法和不确定性量化。这将通过“入门强化课程”、高级培训和每年一度的冬季学校来实现。其次，每个博士生都将学会在一个跨学科的团队中进行沟通和协作。这项培训将从“跨学科欢迎周”开始，并继续由负责每个项目和特殊活动(如研究务虚会)的跨学科PI团队进行。第三，项目范围将就纳入数据和基于DE的建模之间的相互作用提供多种观点，从而有助于加深对数据和模型之间最佳平衡的理解，并从不同角度应对建模过程中数据适应性最佳程度的挑战。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善。因此，我们的RTG将培养新一代跨学科的研究人员，他们在数据科学以及更传统的数学建模和模拟方面受到过高度培训。

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.