Papers › syren-halofit: A fast, interpretable, high-precision formula for the $Λ$CDM nonlinear...
syren-halofit: A fast, interpretable, high-precision formula for the $Λ$CDM nonlinear matter power spectrum
Deaglan J. Bartlett, Benjamin D. Wandelt, Matteo Zennaro, Pedro G. Ferreira, Harry Desmond
Rapid and accurate evaluation of the nonlinear matter power spectrum, P(k), as a function of cosmological parameters and redshift is of fundamental importance in cosmology. Analytic approximations provide an interpretable solution, yet current approximations are neither fast nor accurate relative to numerical emulators. We use symbolic regression to obtain simple analytic approximations to the nonlinear scale, k_σ, the effective spectral index, n_(eff), and the curvature, C, which are required for the halofit model. We then re-optimise the coefficients of halofit to fit a wide range of cosmologies and redshifts. We explore the space of analytic expressions to fit the residuals between P(k) and the optimised predictions of halofit. Our results are designed to match the predictions of EuclidEmulator2, but are validated against N-body simulations. Our symbolic expressions for k_σ, n_(eff) and C have root mean squared fractional errors of 0.8%, 0.2% and 0.3%, respectively, for redshifts below 3 and a wide range of cosmologies. The re-optimised halofit parameters reduce the root mean squared fractional error (compared to EuclidEmulator2) from 3% to below 2% for wavenumbers k=9×10⁻³-9 hMpc⁻¹. We introduce syren-halofit (symbolic-regression-enhanced halofit), an extension to halofit containing a short symbolic correction which improves this error to 1%. Our method is 2350 and 3170 times faster than current halofit and hmcode implementations, respectively, and 2680 and 64 times faster than EuclidEmulator2 (which requires running class) and the BACCO emulator. We obtain comparable accuracy to EuclidEmulator2 and BACCO when tested on N-body simulations. Our work greatly increases the speed and accuracy of symbolic approximations to P(k), making them significantly faster than their numerical counterparts without loss of accuracy.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Tasks
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Methods
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections