Investigation of Algorithms for Highly Nonlinear Model Fitting on Big Datasets

TL;DR

This paper explores algorithms for fitting highly nonlinear models to large datasets, demonstrating a hybrid approach that enables detection of gravitational wave signals in simulated Gaia data.

Contribution

It introduces a hybrid algorithm combining linear search, evolutionary methods, and Gauss-Newton fitting for nonlinear model fitting on big data, applied to gravitational wave detection.

Findings

First detection of gravitational wave signals in simulated Gaia data

Hybrid algorithm effectively handles complex models and large datasets

Software demonstrates potential for real Gaia data analysis

Abstract

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.