At the core of science are two essential components: observation and logic. The former generates data from which we can then use logic to identify regularities and formulate them in the language of mathematics.

Symbolic regression is carried out as a genetic algorithm. Equipped with variables and mathematical operators, the algorithm searches for the simplest mathematical formula with which known data can be reproduced.
To do this, it generates a large number of formulas, compares their predictions with the known data and only adopts formulas that approximate the real data. The surviving formulas are then modified and measured again against each other. At the end of the process there is usually an approximately correct reproduction of the existing data and a simple mathematical formula.

From basic equations of mechanics
Researchers have now used this method to describe the movement of particles and the mass distribution of dark matter . For this they use so-called neural graph networks (GNN) .

These neural networks rely on graphs instead of layers arranged one after the other. Graphs consist of several vertices , which are connected to each other ( edges ). A node contains information that is passed on to the neighboring nodes via the connections and thus changes the state of the receiver point. In this way, each node gradually receives information about the entire graph.

Neural graph networks are particularly well suited for mapping physical systems, since these often consist of the interaction between individual units such as particles . If, for example, the movement of several particles is to be predicted, the nodes store information about the individual particles such as coordinates, last direction of movement and mass.

After the training, the GNN was able to predict the desired property of the halos more accurately than previous models. Using symbolic regression, the researchers were then able to produce a previously unknown mathematical formula that has a lower error rate than the currently most commonly used human-made formula for the same task.

The resulting formula was also better able to deal with previously unknown data. For Cranmer, this is a clear sign that the mathematical formula generalizes much better than the neural graph network from which it was derived. This coincides with our previous experience in physics, says Cranmer: "The language of simple symbolic models describes the universe correctly."

The success of Cranmer and his colleagues shows that the use of AI in research can lead to the discovery of previously unknown formulas . That would make the work of theoretical physicists easier. But the discovery itself is only the first step , after which the new formulas must be combined with known ones and derived. And we still need people to do that - for now.