Exploring supernova gravitational waves with machine learning

Abstract

Gravitational waves from core collapse supernovae offer a unique window into the physics of dense nuclear matter. The bounce signal from rotating stellar cores contains information about the nuclear equation of state, which controls the properties of matter at densities exceeding the density of atomic nuclei. Understanding how well we can extract the information about the equation of state from future detections requires a careful assessment of how detector noise affects machine learning algorithms on classification accuracy and what observational distances permit reliable inference.

This thesis investigates the feasibility of constraining the nuclear equation of state through gravitational wave observations of rotating core collapse using machine learning techniques. We generate a comprehensive dataset of simulated waveforms spanning multiple equations of state, progenitor masses, and rotation rates. We employ both full general relativistic simulations and those using the general relativistic effective potential approximation to assess the impact of gravitational treatment on classification performance.

We apply eight machine learning algorithms: two deep learning architectures (Convolutional Neural Networks and Recurrent Neural Networks) and six classical methods (Random Forest, Support Vector Machines, Naive Bayes, Logistic Regression, k-Nearest Neighbors, and XGBoost). For clean signals without detector noise, Support Vector Machines achieve the highest accuracy of 99.5% when distinguishing among four selected equations of state.

A key finding is that models trained on waveforms from the effective potential approximation cannot reliably classify full general relativistic signals, achieving only 30% accuracy despite 99% performance within their own framework. This demonstrates that training data for equation of state inference must employ full general relativistic simulations rather than computationally cheaper approximations.

To assess realistic observational scenario, we systematically inject detector noise corresponding to Advanced LIGO A+, Einstein Telescope, and Cosmic Explorer sensitivities. Classification accuracy smoothly decline with decreasing signal-to-noise ratio, reaching 87% at SNR = 200 and 68% at SNR = 70 for optimally oriented sources. Random source orientations reduce accuracy by approximately 10%. We establish the distance horizons for reliable equation of state classification: Advanced LIGO A+ can classify equations of state with better than 70% accuracy out to 20 kpc for optimal orientations but only to 10 kpc for random orientations. Next generation detectors extend these horizons to 80-100 kpc for optimal cases and 30 kpc for random orientations.

We also investigate progenitor mass classification and find substantially lower accuracy (approximately 70% at SNR = 100) compared to equation of state identification, reflecting the weak dependence of bounce signals on progenitor mass.

To address the challenge of extracting signals from noisy data, we develop a novel denoising methodology based on autoencoders with Jacobian rank constraints. Unlike conventional autoencoders with fixed dimensionality reduction, our approach incorporates soft rank constraints allowing adaptive adjustment to local data dimensionality. At SNR = 20, autoencoder denoising improves classification accuracy from 24% to 69%, with benefits persisting throughout the low to moderate SNR regime (SNR < 60) that encompasses most observable galactic events.

Our analysis reveals that equation of state inference from core collapse gravitational waves is achievable with current generation detectors for the nearest galactic events under favorable conditions, but reliable classification for typical galactic distances and arbitrary source orientations will require next generation observatories. While our results should be interpreted as approximate upper limits due to simplifying assumptions, they provide quantitative targets for detector sensitivity requirements and demonstrate the scientific potential of multi-messenger observations. The methodology developed in this work establishes a foundation for equation of state inference from future core collapse supernova detections, contributing to our understanding of nuclear matter under the most extreme conditions accessible in nature.