Knowing where and how many things are will help you better understand the cosmos. The largest objects in the universe are clusters of galaxies, which can contain hundreds to thousands of galaxies, as well as plasma, hot gas and dark matter. These elements are bound together by the gravitational pull of the cluster. Understanding such clusters of galaxies is essential to determine the beginnings and continued evolution of the cosmos.

The total mass of a galaxy cluster is perhaps the most important factor in determining its characteristics. Still, estimating this number is challenging because galaxies cannot be “weighed” by placing them on a scale. The fact that dark matter, which makes up a significant portion of a cluster’s mass, is invisible makes it even more difficult. Instead, they infer a cluster’s mass from other measurable characteristics.

Astrophysicists from the Institute for Advanced Study, the Flatiron Institute and collaborators have developed a more accurate method to determine the mass of giant galactic clusters using artificial intelligence. The AI found that scientists could get much better mass estimates than they had by adding a simple term to an existing equation.

Study co-author Francisco Villaescusa-Navarro, a research scientist at the Flatiron Institute’s Center for Computational Astrophysics (CCA) in New York City said: *“It’s that simple; that’s the beauty of this. Even though it is so simple, no one has come across this term before. People have been doing this for decades and yet they couldn’t find this.”*

Called “symbolic regression,” this new AI essentially tries out different combinations of mathematical operators — such as addition and subtraction — with different variables to see which equation best fits the data.

Scientists ‘fed’ their AI algorithm with a state-of-the-art simulation of the universe with different clusters of galaxies. Then Miles Cranmer, a CCA researcher, used their program to search for and identify additional variables that could improve the mass estimates.

Digvijay Wadekar of the Institute for Advanced Study in Princeton, New Jersey, said: *“At the moment, much of the machine learning community focuses on deep neural networks. These are very powerful, but the downside is that they are almost black boxes. We cannot understand what is going on inside them.”*

*“If something in physics gives good results, we want to know why it does that. Symbolic regression is useful because it searches through a given data set and generates simple mathematical expressions in the form of simple equations that you can understand. It provides an easily interpretable model.”*

By adding a single new term to the current equation, the researchers’ symbolic regression program provided them with a new equation that could more accurately predict the mass of the galaxy cluster. Wadekar and his collaborators then discovered a physical explanation by working backward from this AI-generated equation. They found that the presence of supermassive black holes in the centers of galaxies and other regions of galaxy clusters where mass inferences are less accurate are correlated.

Their new equation reduced the significance of the complicated nuclei in the calculations, which improved the mass estimates. The cluster of galaxies resembles a donut in shape. The new equation eliminates the jelly in the center of the donut, which can cause greater inaccuracies, and instead focuses on the doughy edges for more accurate mass inferences.

Using tens of thousands of simulated universes from the CCA’s CAMELS suite, the researchers tested the equation discovered by AI. Compared to the currently used equation, they found that the equation reduced the variability in galaxy cluster mass estimates by about 20 to 30 percent for large clusters.

Wadekar noted, *“The new equation may provide observational astronomers who are conducting upcoming studies of galaxy clusters with better insights into the masses of the objects they observe. There are quite a few surveys focused on galaxy clusters. [that] are planned in the near future.”*

*“Examples include the Simons Observatory, the Stage 4 CMB experiment, and an X-ray study called eROSITA. The new equations can help us maximize the scientific yield of these studies.”*

**Magazine reference:**

- Digvijay Wadekar et al. Improving astrophysical scaling relations with machine learning: application to reducing the Sunyaev-Zeldovich flux mass scattering. Proceedings of the National Academy of Sciences. DOI: 10.1073/pnas.2202074120