Investigations into new machine learning techniques for gravitational wave astronomy

引力波天文学领域目前正受益于机器学习应用在分类(检测或模型选择)和回归(参数估计)等问题上的快速增长。到目前为止，只对引力波数据分析的这些领域进行了研究，因为它们与最常见和成熟的机器学习过程之间存在直接关系。在这个项目中，我们建议研究一种新的(已知的)机器学习形式，称为物理信息神经网络(PINN)，其中机器学习被用于获得精确的函数模型，这些函数是物理信息问题的特定解决方案。例如，这些问题包括由爱因斯坦广义相对论模拟的引力波形，中子星的托尔曼·奥本海默·沃尔科夫方程的解，求解广义相对论时空中粒子的测地线路径，以及求解任意质量-能量分布的时空度规。学生将在引力波场的这些问题和其他问题中研究PINN的可能性。

The field of gravitational wave astronomy is currently benefiting from the rapid growth of machine learning applications to problems such as classification (detection or model selection) and regression (parameter estimation). So far, only these areas of gravitational wave data analysis have been investigated since there is a direct relation between them and the most common and well established machine learning processes. In this project we propose the investigation of a new (known) form of machine learning known as Physics Informed Neural Networks (PINNs) in which machine learning is used to obtain accurate models of functions that are particular solutions to physically informed problems. For example, such problems include gravitational waveforms modelled by Einsteins General Relativity, solutions to the Tolman Oppenheimer Volkoff Equation for neutron stars, solving geodesic paths for particles in a general relativistic spacetime, and solving the spacetime metric for arbitrary mass-energy distributions. The student will investigate the potential for PINNs amongst these and other problems in the gravitational wave field.