The two "fans" on the map represent the main regions studied by the DESI instrument, which is positioned above and below the plane of the Milky Way. Installed on the 4-meter Nicholas U. Mayall Telescope at the Kitt Peak National Observatory (KPNO), DESI has created the largest three-dimensional map of the Universe to date, used for studying dark energy. Earth is located at the center of these two fans, and the bluer points on the map indicate the most distant objects. The image is a frame from an animation showing the rotation of the DESI data map after three years of observations.

Compared to the scale of the Universe, our galaxy is just a tiny dot, which, along with many other dots, forms clusters. These clusters combine into superclusters, which then connect into filaments threaded with voids, creating the gigantic three-dimensional "skeleton" of the Universe.

To build theoretical models such as EFTofLSS (Effective Field Theory of Large-Scale Structure), scientists use the physics of the Universe and data from astronomical instruments. These models allow researchers to statistically describe the "cosmic web" and estimate its key parameters based on observations. However, such calculations require significant computational resources and time. As the volume of astronomical data grows, it becomes essential to speed up analysis without sacrificing accuracy. To achieve this, emulators are used—they mimic the behavior of models but perform calculations much faster.

An international team of experts from INAF (Italy), the University of Parma (Italy), and the University of Waterloo (Canada) has published a study in the Journal of Cosmology and Astroparticle Physics (JCAP) dedicated to testing the Effort.jl emulator. The results showed that Effort.jl delivers nearly the same accuracy as the original model, and sometimes even more detailed results, while running in just a few minutes on a regular laptop instead of requiring a supercomputer.

The Effort.jl emulator uses a neural network trained on precomputed model predictions and can generalize results to new combinations of parameters. What sets Effort.jl apart is that its algorithm is initially designed with knowledge of how predictions change with varying parameters and also utilizes gradients. This allows it to learn from fewer examples and reduces computational costs.

Validation conducted in the study demonstrated that Effort.jl’s accuracy on both simulated and real data is close to that of the original model. In some cases, the emulator made it possible to include elements in the analysis that previously had to be omitted to speed up calculations. Effort.jl could become an important tool for analyzing new data from DESI and Euclid experiments, which will significantly expand our understanding of the large-scale structure of the Universe.

The study “Effort.jl: a fast and differentiable emulator for the effective field theory of large-scale structure of the Universe” was published in the Journal of Cosmology and Astroparticle Physics (JCAP).