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A geometric physics-informed machine learning inference for the neutron star maximum mass and the inverse problem
High Energy Astrophysical Phenomena · Submitted 20 Feb 2026 · Published version
abstract compiled · 2026-10-26 · no language-model review
The authors' main claim 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 neutron star of $1.4$ solar masses.
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The abstract, sentence by sentence
The existence of a distinct mass boundary between the heaviest neutron stars and the lightest black holes remains in question. It is an artefact of our ignorance of the properties of matter at supra-nuclear densities, which exist in the cores of neutron stars. The study addresses these problems with 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 transformer provides a two-step solution: first, the model predicts the maximum mass and radius using the bending parameters. Second, it predicts the square of the sound speed profile, completing the inverse mapping. The prediction is that massive neutron stars form when the sound speed peaks at low density, leading to strong back-bending and an early phase transition to quark matter. Massive stars favour a stiff equation of state at low density, and the density of matter at the star's core is sufficiently small. 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 neutron star of $1.4$ solar masses.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The existence of a distinct mass boundary between the heaviest neutron stars and the lightest black holes remains in question. | gap 0.55 | 0.04 | 0.03 | asserted 0.45 |
| s1 | It is an artefact of our ignorance of the properties of matter at supra-nuclear densities, which exist in the cores of neutron stars. | background 0.58 | 0.05 | 0.03 | asserted 1.00 |
| s2 | The study addresses these problems with a physics-informed machine learning approach, guided by astrophysical observations. | contribution 0.86 | 0.78 | 0.04 | asserted 0.99 |
| s3 | The Transformer model is trained on an agnostically generated ensemble of equations of state. | method 1.00 | 0.86 | 0.02 | asserted 1.00 |
| s4 | Two geometric parameters are defined on the mass-radius sequence of a neutron star--the front bending and the back bending. | method 0.77 | 0.86 | 0.03 | asserted 1.00 |
| s5 | The transformer provides a two-step solution: first, the model predicts the maximum mass and radius using the bending parameters. | method 0.98 | 0.84 | 0.10 | asserted 1.00 |
| s6 | Second, it predicts the square of the sound speed profile, completing the inverse mapping. | method 0.98 | 0.82 | 0.08 | asserted 1.00 |
| s7 | The prediction is that massive neutron stars form when the sound speed peaks at low density, leading to strong back-bending and an early phase transition to quark matter. | interpretation 0.74 | 0.79 | 0.47 | asserted 0.87 |
| s8 | Massive stars favour a stiff equation of state at low density, and the density of matter at the star's core is sufficiently small. | interpretation 0.87 | 0.54 | 0.13 | asserted 0.99 |
| s9 | 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 neutron star of $1.4$ solar masses. | result 1.00 | 0.91 | 0.46 | asserted 0.99 |
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Original abstract
The existence of a distinct mass boundary between the heaviest neutron stars and the lightest black holes remains in question. It is an artefact of our ignorance of the properties of matter at supra-nuclear densities, which exist in the cores of neutron stars. The study addresses these problems with 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 transformer provides a two-step solution: first, the model predicts the maximum mass and radius using the bending parameters. Second, it predicts the square of the sound speed profile, completing the inverse mapping. The prediction is that massive neutron stars form when the sound speed peaks at low density, leading to strong back-bending and an early phase transition to quark matter. Massive stars favour a stiff equation of state at low density, and the density of matter at the star's core is sufficiently small. 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 neutron star of $1.4$ solar masses.
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