Coordination Funds

在这个研究单元中，我们将研究测地学的两个核心领域中基本人工智能问题的算法挑战，这两个领域都涉及现实世界的几何抽象：制图和物理大地测量学。我们方法的一个中心特征是专注于固有的几何数据表示，目的是研究问题的本机形式。对人工智能问题潜在算法挑战的系统研究是算法数据分析领域的中心任务。因此，该研究单位汇集了算法数据分析领域和上述两个大地测量领域的专家。作为两端之间的调解人，我们看到了计算几何和算法工程领域，特别是处理这些领域已经建立的问题的方法。计算几何学将几何现实世界的数据转换为离散配置，从而使离散优化技术的应用成为可能。算法工程带来了从理论分析到实际应用的一整套知识传递过程。作为项目成果，我们希望获得新的数据分析方法，以应对大地测量人工智能问题的具体挑战。我们的新方法将针对给定的问题量身定做，并且通常伴随着可证明的性能保证。他们可以使用新的算法工程和组合优化技术，建立在输入的几何结构上。正在进行的对来自大地测量的实际实际数据的实验评估将稳步导致应用方法的理论和实践改进。我们的中心目标是大幅缩小当前人工智能研究和大地测量学之间的差距，并在这两个学科之间建立持久的联系。这将使未来关于大地测量自动化的研究能够在更坚实的算法基础上进行。同时，我们的研究单位将推进机器学习工具对几何表示数据和相应距离度量的算法理解。我们将开发一系列精心设计的算法和实现，即使对于非常大的数据集，在几何边约束和多目标的情况下，也能够利用数据的几何结构。我们相信，我们的方法不仅会让大地测量学的研究人员感兴趣，而且会对涉及几何数据分析的任何其他领域感兴趣。

Within this research unit, we will study the algorithmic challenges of fundamental artificial intelligence problems in two central areas of geodesy that both deal with geometric abstractions of the real world: cartography and physical geodesy. A central characteristic of our approach is a focus on an inherently geometric data representation motivated by the aim to study the problems in their native form. The systematic study of the underlying algorithmic challenges of AI problems is a central task in the field of algorithmic data analytics. This research unit thus brings together experts in the area of algorithmic data analytics and in the above two mentioned areas of geodesy. As a mediator between the two ends we see the fields of computational geometry and algorithm engineering, in particular the way to approach problems that these fields have established. Computational geometry transfers geometric real-world data into discrete configurations, thereby enabling the application of discrete optimization techniques. Algorithm engineering brings a whole routine of transferring knowledge between theoretical analysis and practical applications. As project outcome we expect to obtain new data analytics methods that deal with the specific challenges of geodetic AI problems. Our new methods will be tailored to the given problems and usually be accompanied with provable performance guarantees. They may use new algorithm engineering and combinatorial optimization techniques building on the geometric structure of the input. An ongoing experimental evaluation on practical real-world data from geodesy will steadily lead to theoretical as well as practical improvement of the applied methods. Our central goal is to substantially close the gap between current research in artificial intelligence and geodesy and to establish persistent links between the two disciplines. This will allow future research on automation in geodesy to be conducted on a more solid algorithmic basis. At the same time, our research unit will advance the algorithmic understanding of machine learning tools for geometrically represented data and corresponding distance measures. We will develop a collection of carefully designed algorithms and implementations that are able to exploit the geometric structure of the data even for very large data sets, under geometric side constraints and for multiple objectives. We are convinced that our approach will not only be interesting to researchers in geodesy but to any other area that involves the analysis of geometric data.