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Mapping neutron star observations to the equation of state: a bayesian neural network approach

Authors: Valéria Maria Dinis Carvalho

Ref.: MSc in Physics (2023)

Abstract: Neutron Star (NS)s stand out as uniquely compelling astrophysical objects for comprehending and constraining the Equation of State (EoS) of nuclear matter. These objects, subjected to extreme con- ditions, offer a unique opportunity to explore uncharted territories within the Quantum Chromody- namics phase diagram. However, the challenge persists in translating observations of NSs into mean- ingful insights about their composition and the corresponding EoS. The limited and uncertain nature of available observations further compounds this issue. Addressing this crucial problem necessitates a tool capable of directly mapping NS observations to the EoS while being aware of inherent data uncertainties. Herein, we aim to achieve this objective through the application of Bayesian Neural Network (BNN)s. While machine learning methodologies, even more so neural networks, have previ- ously ventured into addressing the task of mapping observations to the EoS, a critical aspect has been missing: the ability to capture uncertainty. This is where BNNs emerge as a groundbreaking solution, capable of not only establishing connections between observations and the EoS but also encapsulat- ing uncertainties within both the model and the dataset. In pursuit of this goal, we train our BNN models using a comprehensive dataset encompassing 25,000 nuclear EoS within the Relativistic Mean Field (RMF) framework. This dataset is constructed through Bayesian inference, constrained by minimal low-density constraints. Spanning NS observables such as radius, mass, and tidal deformability, this dataset gives insights into the proton fraction and sound speed within these enigmatic interiors. To replicate real-world observations, we’ve introduced mod- ifications to the dataset employed by incorporating noise into the input vector of our model. This was done in four different ways for both the training and testing datasets. Our results demonstrate the BNN models accurately correlate observations with the intrinsic properties of NSs, all while pro- viding a quantifiable measure of the uncertainty. This achievement remains consistent even when the model is tested with simulated data from the DD2 dataset, a class that also belongs to the RMF models but with density-dependent couplings, used to generate the EoS used to test the BNN model. Keywords: Neutron Stars, Bayesian Neural Networks, Uncertainty Quantification, Equation of state

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