# syren-new: Precise formulae for the linear and nonlinear matter power spectra with massive neutrinos and dynamical dark energy

arXiv: https://arxiv.org/abs/2410.14623 · HTML: https://mlsanity.com/paper/2410.14623/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 15 references that are in the map.
- First posted on arXiv 18 Oct 2024.

## Builds on (most cited first, 1 of 1)

- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)

## Built on by (most cited first, 4 of 4)

- [(Exhaustive) Symbolic Regression and model selection by minimum description length](https://mlsanity.com/paper/2507.13033/) (2025)
- [Exploring Multi-view Symbolic Regression methods in physical sciences](https://mlsanity.com/paper/2509.10500/) (2025)
- [Symbolic Emulators for Cosmology: Accelerating Cosmological Analyses Without Sacrificing Precision](https://mlsanity.com/paper/2510.18749/) (2025)
- [Don't Cut Corners: How Training Outside the Prior Makes Simulation-Based Inference More Robust](https://mlsanity.com/paper/2608.12470/) (2026)

## Abstract (arXiv)

Current and future large scale structure surveys aim to constrain the neutrino mass and the equation of state of dark energy. We aim to construct accurate and interpretable symbolic approximations to the linear and nonlinear matter power spectra as a function of cosmological parameters in extended LambdaCDM models which contain massive neutrinos and non-constant equations of state for dark energy. This constitutes an extension of the syren-halofit emulators to incorporate these two effects, which we call syren-new (SYmbolic-Regression-ENhanced power spectrum emulator with NEutrinos and W0-wa). We also obtain a simple approximation to the derived parameter σ8 as a function of the cosmological parameters for these models. Our results for the linear power spectrum are designed to emulate CLASS, whereas for the nonlinear case we aim to match the results of EuclidEmulator2. We compare our results to existing emulators and N-body simulations. Our analytic emulators for σ8, the linear and nonlinear power spectra achieve root mean squared errors of 0.1%, 0.3% and 1.3%, respectively, across a wide range of cosmological parameters, redshifts and wavenumbers. We verify that emulator-related discrepancies are subdominant compared to observational errors and other modelling uncertainties when computing shear power spectra for LSST-like surveys. Our expressions have similar accuracy to existing (numerical) emulators, but are at least an order of magnitude faster, both on a CPU and GPU. Our work greatly improves the accuracy, speed and range of applicability of current symbolic approximations to the linear and nonlinear matter power spectra. We provide publicly available code for all symbolic approximations found.