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，只有这些引力波数据分析领域得到了研究，因为它们与最常见和最完善的机器学习过程之间存在直接关系。在这个项目中，我们提出了一种新的（已知的）机器学习形式的研究，称为物理信息神经网络（pinn），其中机器学习用于获得函数的精确模型，这些模型是物理信息问题的特定解决方案。例如，这些问题包括爱因斯坦广义相对论所模拟的引力波，求解中子星的托尔曼奥本海默沃尔科夫方程，求解广义相对论时空中粒子的测地路径，以及求解任意质能分布的时空度规。学生将在引力波场的这些问题和其他问题中研究pin n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.