Parameterizing Gravitational Waveform Uncertainty for Machine Learning Training Data

In our universe, the collisions of extremely dense objects, such as neutron stars, create ripples through space. These ripples are gravitational waves that expand and compress the space they travel through. We can detect these waves using interferometers, like the LIGO detectors. However, gravitational waves have intrinsic uncertainties between the true waveform we detect from space and the waveform models, or waveform approximants, we use for parameter estimation. These uncertainties can be quantified in amplitude and phase, δA and δφ. Our goal is to use machine learning to pick out the differences between two approximants using the uncertainties between them. This requires a large set of training data to be given to the program. Training data provides information in the machine learning process, helping us further with our analysis. Our training data utilizes GW170817 sample sets and includes: a range of frequencies relevant to gravitational wave detection, neutron star source parameters, amplitude uncertainty, and phase uncertainty for each waveform. Large orders of magnitude in the data handled in the computation emphasizes the necessity for optimization. The largest step of optimization was reducing the size of the waveform uncertainty data, which were the largest parts of the dataset. We wanted each uncertainty to be expressed in 10 parameters, a number small enough to be run through machine learning quickly. This was achieved utilizing a series of Chebyshev polynomials and uncertainties in the LIGO detectors, allowing for a concise parameterization of waveform uncertainty.