Mapping the universe, faster and with the same accuracy

If you think a galaxy is big, compare it to the size of the universe: it’s just a tiny dot which, together with a huge number of other tiny dots, forms clusters that aggregate into superclusters, which in turn weave into filaments threaded with voids—an immense 3D skeleton of our universe.

If that gives you vertigo and you’re wondering how one can understand or even “see” something so vast, the answer is: it isn’t easy. Scientists combine the physics of the universe with data from astronomical instruments and build theoretical models, such as EFTofLSS (Effective Field Theory of Large-Scale Structure). Fed with observations, these models describe the “cosmic web” statistically and allow its key parameters to be estimated.

Models like EFTofLSS, however, demand a lot of time and computing resources. Since the astronomical datasets at our disposal are growing exponentially, we need ways to lighten the analysis without losing precision. This is why emulators exist: they “imitate” how the models respond, but operate much faster.

Since this is a kind of “shortcut,” what’s the risk of losing accuracy?

An international team including, among others, INAF (Italy), The University of Parma (Italy) and the University of Waterloo (Canada) has published in the Journal of Cosmology and Astroparticle Physics a study testing the emulator Effort.jl, which they designed. The study is titled “Effort.jl: a fast and differentiable emulator for the Effective Field Theory of the Large Scale Structure of the Universe.”

It shows that Effort.jl delivers essentially the same correctness as the model it imitates—sometimes even finer detail—while running in minutes on a standard laptop instead of a supercomputer.

“Imagine wanting to study the contents of a glass of water at the level of its microscopic components, the individual atoms, or even smaller: in theory you can. But if we wanted to describe in detail what happens when the water moves, the explosive growth of the required calculations makes it practically impossible,” explains Marco Bonici, a researcher at the University of Waterloo and first author of the study.

“However, you can encode certain properties at the microscopic level and see their effect at the macroscopic level, namely the movement of the fluid in the glass. This is what an effective field theory does, that is, a model like EFTofLSS, where the water in my example is the universe on very large scales and the microscopic components are small-scale physical processes.”

The theoretical model statistically explains the structure that gives rise to the data collected: the astronomical observations are fed to the code, which computes a “prediction.” But this requires time and substantial compute. Given today’s data volume—and what is expected from surveys just begun or coming soon (such as DESI, which has already released its first batch of data, and Euclid)—it’s not practical to do this exhaustively every time.

“This is why we now turn to emulators like ours, which can drastically cut time and resources,” Bonici continues.

An emulator essentially mimics what the model does: its core is a neural network that learns to associate the input parameters with the model’s already-computed predictions.

The network is trained on the model’s outputs and, after training, can generalize to combinations of parameters it hasn’t seen. The emulator doesn’t “understand” the physics itself: it knows the theoretical model’s responses very well and can anticipate what it would output for a new input.

Effort.jl’s originality is that it further reduces the training phase by building into the algorithm knowledge we already have about how predictions change when parameters change: instead of making the network “re-learn” these, it uses them from the start.

Effort.jl also uses gradients—i.e., “how much and in which direction” predictions change if you tweak a parameter by a tiny amount—another element that helps the emulator learn from far fewer examples, cutting compute needs and allowing it to run on smaller machines.

A tool like this needs extensive validation: if the emulator doesn’t know the physics, how sure are we that its shortcut yields correct answers (i.e., the same ones the model would give)? The newly published study answers exactly this, showing that Effort.jl’s accuracy—on both simulated and real data—is in close agreement with the model.

“And in some cases, where with the model you have to trim part of the analysis to speed things up, with Effort.jl we were able to include those missing pieces as well,” Bonici concludes.

Effort.jl thus emerges as a valuable ally for analyzing upcoming data releases from experiments like DESI and Euclid, which promise to greatly deepen our knowledge of the universe on large scales.