syren-baryon: Analytic emulators for the impact of baryons on the matter power spectrum

TL;DR

This work develops analytic emulators for the impact of baryons on the matter power spectrum by learning models for the suppression factor $S(k,z,\bm{\theta})$ with symbolic regression. It treats four CAMELS hydrodynamical models (Astrid, IllustrisTNG, SIMBA, Swift-EAGLE) and a baryonification scheme, providing separate $S$-functions per model and an uncertainty description tied to sample variance. The approach enforces correct large-scale and high-redshift limits, delivers percent-level accuracy (0.7% RMSE for the baryonification emulator), and yields interpretable dependencies on cosmological and feedback parameters, enabling model discrimination and direct incorporation into cosmological analyses. Public Python implementations of the derived expressions are provided, offering a portable, analytic alternative to computationally expensive simulations for upcoming survey analyses.

Abstract

Baryonic physics has a considerable impact on the distribution of matter in our Universe on scales probed by current and future cosmological surveys, acting as a key systematic in such analyses. We seek simple symbolic parametrisations for the impact of baryonic physics on the matter power spectrum for a range of physically motivated models, as a function of wavenumber, redshift, cosmology, and parameters controlling the baryonic feedback. We use symbolic regression to construct analytic approximations for the ratio of the matter power spectrum in the presence of baryons to that without such effects. We obtain separate functions of each of four distinct sub-grid prescriptions of baryonic physics from the CAMELS suite of hydrodynamical simulations (Astrid, IllustrisTNG, SIMBA and Swift-EAGLE) as well as for a baryonification algorithm. We also provide functions which describe the uncertainty on these predictions, due to both the stochastic nature of baryonic physics and the errors on our fits. The error on our approximations to the hydrodynamical simulations is comparable to the sample variance estimated through varying initial conditions, and our baryonification expression has a root mean squared error of better than one percent, although this increases on small scales. These errors are comparable to those of previous numerical emulators for these models. Our expressions are enforced to have the physically correct behaviour on large scales and at high redshift. Due to their analytic form, we are able to directly interpret the impact of varying cosmology and feedback parameters, and we can identify parameters which have little to no effect. Each function is based on a different implementation of baryonic physics, and can therefore be used to discriminate between these models when applied to real data. We provide publicly available code for all symbolic approximations found.

Figures (6)

• Figure 1: The baryonic effect, $\log S$ (\ref{['eq:S_definition']}), on the power spectrum for the 27 CV simulations and its standard deviation over $k$ for the Astrid sub-grid model at $z = 0$.
• Figure 2: Difference between the symbolic fits for the baryonic effect on the power spectrum ($S_{\rm pred}$) to the true values ($S$) from the test set. Each column is for a difference baryonic model, and each row is for a different redshift, $z$. The solid lines indicate the mean difference and the shaded region contains 68% of samples. In the dashed orange lines we show the symbolic fits to the error on our models, as given in \ref{['tab:sigma_fits']}. This error is due to a combination of stochasticity in the simulation and imperfect symbolic approximations.
• Figure 3: Extrapolation behaviour of our symbolic models for redshifts, $z$, and wavenumbers, $k$, outside of the range of the training data. The models are evaluated at the fiducial cosmological and astrophysical parameters (\ref{['tab:baryonification_prior', 'tab:hydro_prior']}). As required physically, the correction to the power spectrum, $S$, becomes unity at high redshift and on large scales (small $k$).
• Figure 4: Predicted baryonic suppression of the matter power spectrum, $S$, as a function of wavenumber, $k$, at redshift zero for four randomly sampled hydrodynamical simulations at $z=0$. Our predictions from \ref{['tab:fits']} are shown as solid lines, and the shaded regions give the estimated error on these from \ref{['tab:sigma_fits']}. The dashed lines give the true values measured from the simulations, which are seen to be consistent with our predictions.
• Figure 5: Pareto front of solutions found with operon for $\log S$ (\ref{['eq:S_definition']}). We plot the training and test sets separately, and the dashed lines indicates our chosen models.