In the center of a galaxy cluster, the gas is heated to a hundred million degrees. Galaxy clusters are giant clouds of hundreds of galaxies and diffuse gas, held together by gravity. As early as the 1930s, astronomer Fritz Zwicky noticed that galaxies in these clouds move too fast, as if attracted by something invisible. Later, Vera Rubin confirmed this discovery for individual galaxies. This is how dark matter was discovered — an invisible substance that emits no light but makes up about 85% of all mass. To measure this hidden mass, astronomers study the hot gas, which glows brightly in X-ray radiation (super-high-energy rays).

Each cluster can be imagined as a book, whose pages are layers of gas from the center to the edge. On these pages are recorded temperature, density, and pressure. Previously, scientists read each page separately, assuming the gas is in perfect equilibrium, like water in a still glass. But when a cluster collides with a neighbor, equilibrium is disrupted and calculations go wrong. A new Machine Learning model (a trainable computer program) works differently. It reads the book sequentially, remembering previous pages, and thus grasps the overall plot. It was trained on 16 495 virtual clusters from a numerical simulation (a digital model of the Universe). Now the network takes data on temperature, density, entropy (a thermal property of the gas) layer by layer and outputs the total mass without any assumptions about calm.

The accuracy is impressive: the error is about 5%—twice as good as older methods that failed in turbulent systems. The network was tested on real X-ray survey data, including spectroscopy measurements (analysis of radiation composition) and redshift measurements (spectral shift due to cosmic expansion). It turned out that the classical approach systematically underestimated the mass of the most massive clusters by about 10%. Interestingly, the network remains accurate even when accounting for additional complex processes, such as feedback from active galactic nucleus (supermassive black holes at the center).

Now the neural network is ready to work with future large-scale surveys that will capture hundreds of thousands of clusters. This will make cosmology much more accurate: we will be able to objectively calibrate the relationship between mass and observable properties, and thus better understand the nature of dark matter and dark energy. So the first book from the great library of the Universe has been read, and its plot is so clear that it's time to turn the page.