Inferring the neutron star equation of state using Machine Learning methods

Irwin, Jessica (2025) Inferring the neutron star equation of state using Machine Learning methods. PhD thesis, University of Glasgow.

Abstract

The first decade of gravitational wave (GW) detection using the global ground based GW detector network has facilitated a new era of neutron star observation. From the GW signal produced when two neutron stars (NSs) inspiral and merge, one can directly measure the masses of the two NSs and, importantly, their tidal deformability, a direct measure of the behaviour of matter in the system. This parameter is unique to GW astronomy and therefore offers an independent method to infer the neutron star (NS) equation of state. Due to lack of precision in measurement of NS macroscopic parameters, the equation of state – the relationship between the pressure and density within the ultra-dense neutron-rich matter of a neutron star – is still widely unknown. Though there are various inference schemes to infer the NS equation of state given electromagnetic (EM) and GW observation, these are often computationally and temporally expensive processes.

Recently, the introduction of machine learning (ML) tools in astronomical data analysis have facilitated the handling of large amounts of data and the processing of this data efficiently, to find broad trends or features. These tools will become necessary when considering future GW detection, where we expect increased sensitivity of detectors as well as orders of magnitude more detections, including those of binary neutron star (BNS) mergers. In this thesis, we apply ML methods, notably a type of generative ML model called a Normalising Flow, in developing tools through which we can infer the NS equation of state in current and future observation of gravitational waves (GWs) from BNS mergers.

We firstly introduce a Normalising Flow trained to perform the mapping of equation of state data conditioned on BNS event parameters. Once trained, the Flow can be conditionally sampled to return an equation of state posterior given posterior samples from a single GW event in less than 1 second. Simulation studies demonstrate the validity of the Flow result, alongside the equation of state posterior for the GW event GW170817, which is in agreement with the existing accepted result. The tool facilitates rapid follow-up of GWs from BNS mergers for improved communication with EM astronomers.

In setting the scene for hierarchical inference of the NS equation of state given multiple observations of GWs from BNS mergers, we discuss the performance of Normalising Flows in mapping complex high-dimensionality data sets. The introduction of a new equation of state training data set makes use of an autoencoder for data compression, which achieves root-mean-squared (RMS) error on the equation of state reconstruction on the scale of 10⁻³ for normalised mean-subtracted equations of state. We demonstrate abnormalities in the Normalising Flow’s performance in mapping regions of the equation of state space, which manifests as severe spikes and troughs of probability. We highlight the dangers of inconsiderate application of Normalising Flows to mapping any high-dimensionality data set. We finally introduce the regeneration Flow, built to learn the mapping of the joint data and conditional spaces at once, such that it can be sampled repeatedly during training for unlimited training data generation. We demonstrate how this improves Normalising Flow training and reduces the fluctuations in magnitude of probability over the surface of the learned data space, promoting generic learning.

We apply the improved Normalising Flow to hierarchical analysis of the neutron star equation of state, firstly in inferring the combined equation of state given the first two BNS merger observations. We make use of a full ML parameter estimation (PE) pipeline to perform a simulation study of inferring the true equation of state given multiple simulated BNS events associated to three known equations of state. We demonstrate that as we increase the number of events, the quality of sampling the equation of state posterior decreases, suggesting a highly multi-modal space and/or inaccurate model. We introduce an alternative method for hierarchical inference which is more robust by using the Normalising Flow instead to sample. With the new method, the result of combining information from up to 16 BNS events associated to two out of three simulated equations of state produce a constrained equation of state posterior which agrees with the truth. We highlight the computational expense of the workflow; inference of up to 16 events with the new method takes less than 1 hour. This validates the use of Normalising Flows for hierarchical inference of the NS equation of state in future observing runs, when the number of events are expected to be in the 10s. We suggest substantial future work to improve the sampling quality and, beyond this, tests for the next generation of GW detection to validate the use of Normalising Flows in understanding neutron star matter.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Subjects: Q Science > QB Astronomy; Q Science > QC Physics
• Colleges/Schools: College of Science and Engineering > School of Physics and Astronomy
• Supervisor's Name: Heng, Professor Ik Siong and Messenger, Dr. Christopher
• Date of Award: 2025
• Depositing User: Theses Team
• Unique ID: glathesis:2025-85651
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 12 Dec 2025 10:01
• Last Modified: 12 Dec 2025 10:08
• Thesis DOI: 10.5525/gla.thesis.85651
• URI: https://theses.gla.ac.uk/id/eprint/85651