大数据集高度非线性模型拟合算法研究
Investigation of Algorithms for Highly Nonlinear Model Fitting on Big Datasets
摘要：
本论文研究了关于大数据集高度非线性模型拟合的适用性的算法。提出了各种数学方法，可以使用最小二乘准则进行模型拟合。讨论了作为这种模型拟合的基础的大型数据集的处理的特殊要求。在欧空局卫星任务盖亚的模拟数据中搜索引力波信号的具体例子被用来演示模型拟合是如何可能的，即使是复杂的模型和大量的数据。为了这个目的，一个高度并行的原型，未来的搜索软件实现。由此产生的原型使用的混合算法，利用线性搜索，进化算法和经典的迭代高斯-牛顿拟合。详细研究了其组成部分的性能和行为。借助本文提出的软件，首次在模拟天体测量数据中探测到了引力波信号，并确定了它们的参数。此外，从软件的运行时行为可以得出结论，在盖亚任务的实际数据中也可以进行这种搜索。
英文摘要：
This thesis investigates algorithms regarding their applicability for highly nonlinear model fitting on big datasets. Various mathematical methods are presented with which a model fit using the least squares criterion is possible. Special requirements regarding the processing of large data sets as a basis for such a model fit are discussed. The specific example of the search for gravitational wave signals in simulated data of the ESA satellite mission Gaia is used to demonstrate how a model fit is possible, even with complex models and large amount of data. For this purpose, a highly parallel prototype of a future search software is implemented. The resulting prototype uses a hybrid algorithm which utilizes a linear search, an evolutionary algorithm and a classical iterative Gauss-Newton fit. The performance and behavior of its components are investigated in detail. With the help of software presented in this work it has been possible for the first time to detect gravitational wave signals in simulated astrometric data, and to determine their parameters. Furthermore, it can be concluded from the runtime behavior of the software that such a search is also possible in real data of the Gaia mission.
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