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What's Inside a Neutron Star: AI Reveals It by Weight and Size

Original: "Constraining the High-Density Equation of State with Present and Future NICER Observations Using Physics-Informed Regularized Machine Learning"
arXiv:2607.12722 · 2026-07-14 · CC BY 4.0 · 1 min · High Energy
Artificial intelligence reveals the interior of neutron stars in a second from their mass and radius.
Abstract

Scientists have created a neural network that, from the mass and size of a neutron star, instantly calculates what pressure and density are hidden in its depths—just as from a person's height and weight you can guess their build. The network is trained to obey the laws of physics so that the answers are correct. It turned out that the best clues come from observing two types of stars. What else will these cosmic lighthouses tell us?

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Neutron stars are the remnants of dead giants, crushed into a sphere the size of a city. Their mass and radius are known from observations of lighthouse-like pulsars and gravitational waves (ripples in space), picked up by the LIGO observatory using giant laser 'rulers'. But the composition of their interiors remains a mystery—like trying to guess the fruit inside a sealed box just by its weight and size. The old method was like brute-forcing every conceivable filling with a computer (computer simulations) until one matched.

Inside this 'fruit', sound races almost as fast as light: under monstrous pressure, the speed of sound reaches 60% of the speed of light—only light itself is faster.

Now a neural network trained on thousands of examples instantly spits out pressure and density from mass and radius, like a seasoned gourmand guessing the contents by the box's weight. It strictly obeys the laws of physics, passed down by Einstein, Schwarzschild, and Chandrasekhar. This instant analysis points out which stars to watch first to unravel the secret of the densest matter.

🎯 Under monstrous pressure inside a neutron star, sound travels at 60% the speed of light—180,000 km/s, almost nothing is faster.

🎬 The sci-fi novel 'Dragon's Egg' describes intelligent life on the surface of a neutron star. Today, neural networks help figure out if even hints of such a thing could exist there.

\frac{dP}{dr} = -\frac{G m(r) \rho(r)}{r^2} \left[1+\frac{P(r)}{\rho(r)c^2}\right] \left[1+\frac{4\pi r^3 P(r)}{m(r)c^2}\right] \left[1-\frac{2Gm(r)}{rc^2}\right]^{-1}
Relates the pressure gradient P(r) to the mass m(r), density ρ(r), and radius r within the framework of general relativity.
c_s^2 = \frac{dP}{d\epsilon}
Parameter characterizing the stiffness of the equation of state; must satisfy 0 ≤ c_s^2 ≤ 1.
Scientists
Christian DopplerD. B. McLaughlinDidier QuelozMichel MayorR. A. RossiterAlbert Einstein
Tags
neutron star Machine Learning pulsar gravitational waves speed of light numerical simulation LIGO interferometry
Laws
Doppler effectprinciple of constancy of the speed of lightmass–energy equivalenceEinstein field equationsMaxwell's equationsLorentz transformations
Original: arXiv:2607.12722 · CC BY 4.0 · bridge42worlds