Astronomers, like chefs, have long been preparing a description of the Universe using the same cumbersome recipes. These recipes — complex mathematical formulas — estimated how many galaxies of different luminosity and mass fill the cosmos, as well as how the invisible frameworks of dark matter are distributed. But the dishes lacked accuracy. So, a digital head chef was called into the kitchen — the ESR algorithm. It tested millions of variations from simple operations: addition, multiplication, exponentiation.
The result was stunning: it turned out that bells and whistles aren't needed for the perfect outcome. Simple relationships — for example, 'the brighter the galaxy, the fewer there are' — work more accurately if artificial corrections are removed. It's like discovering that a croissant only needs three ingredients, and it tastes better than a complex recipe. Now astronomers can piece together the puzzle of galaxy history faster and refine the standard cosmological model.
as written by the authors arXiv:2604.23236
The galaxy luminosity and stellar mass function (LF, SMF), and halo mass function (HMF), are fundamental quantities in astrophysics and crucial inputs to a range of astrophysical and cosmological analyses. They are typically parametrised by fitting functions that have been chosen "by eye" to match observed or simulated data. We apply symbolic regression -- specifically the Exhaustive Symbolic Regression (ESR) algorithm -- to automate the search for optimal LF, SMF and HMF functional forms. ESR scores all functions up to a maximum complexity composed of a user-defined basis set of operators using the description length, an approximation to the Bayesian evidence that balances accuracy with complexity. We find many functions outperforming the Schechter and double Schechter functions for the LF and SMF, and that outperform the Press--Schechter and Warren/Tinker functions for the HMF. By additionally imposing "physicality checks" on functions' extrapolation and integration properties, we identify the optimal, low-complexity functional forms in terms of accuracy, simplicity and behaviour beyond the data range. As well as providing drop-in replacements for literature LF, SMF and HMF fitting functions, and identifying robust behaviour across well-fitting functions, we present a framework with which symbolic regression may be used to automate the discovery of optimal functions for any astrophysical dataset.
Small, dim galaxies vastly outnumber giant bright ones in the Universe — like pebbles on a beach compared to boulders.
Just like in 'The Hitchhiker's Guide to the Galaxy' a supercomputer sought the Answer to the ultimate question, this algorithm seeks the perfect recipe for the cosmos — except instead of philosophy, it yields precise equations.