The quest to understand the properties of matter at supranuclear densities found in the cores of neutron stars has intrigued physicists for a long time. The study addresses this problem using a physics-informed machine learning approach guided by astrophysical observations. The transformer model is trained on an agnostically generated ensemble of equations of state. Two geometric parameters are defined on the mass-radius sequence of a neutron star—the front bending and the back bending. The model provides a two-step solution: first, the model predicts the maximum mass and radius using the bending parameters, and then reconstructs the square of the sound-speed profile, completing the inverse mapping to the equation of state. Our results show that massive neutron stars are associated with sound-speed profiles that peak at relatively low densities, leading to strong back bending and a low-density stiff equation of state, indicating an early transition to quark matter and making the density at the core of massive stars comparatively less. The maximum mass for a neutron star predicted by the astrophysical constrained transformer model is 2.477 solar masses, and a minimum radius of about 11.498 km for a canonical mass of 1.4 solar masses.

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• Equations of state
• Neutron stars & pulsars
• Machine learning