From redshift to real space: Combining linear theory with neural networks

Context. Spectroscopic redshift surveys are key to tracing the large-scale structure (LSS) of the Universe and testing the Λ Cold Dark Matter model. However, redshifts as distance proxies introduce distortions in the 3D galaxy distribution. If uncorrected, these redshift-space distortions (RSDs) lead to systematic errors in LSS analyses and cosmological parameter estimation. Aims. This study aims to develop and assess a new method that combines linear theory (LT) and a neural network (NN) to mitigate RSDs, with testing done on a suite of dark matter halo catalogs. Methods. We present a hybrid reconstruction method (LT + NN) combining linear perturbation theory with a NN trained to map halo fields from redshift to real space using a mean squared error (MSE) loss. Training and validation were performed on halo fields from z = 1 snapshots of the Quijote N-body simulations. LT corrects large-scale distortions in the linear regime, while the NN captures smaller-scale and quasi-linear features. Training the NN on LT-corrected fields enables accurate reconstruction across scales. Results. The LT + NN method reduces the MSE by ∼50% compared to LT and ∼12% compared to NN alone. The reconstructed fields correlate more tightly with the true real-space fields. Compared to LT, the hybrid method shows marked improvements in the halo-halo and halo-void correlation functions, extending to the baryon acoustic oscillation scale. While gains over NN are smaller, they are statistically significant, especially in reducing anisotropies on large and quasi-linear scales, as seen in the quadrupole of the correlation functions. Conclusions. Combining a physically motivated model with an NN overcomes the limitations of each approach when used separately. This hybrid method offers an effective way to mitigate RSDs with modest training data and computational cost, supporting future applications to more realistic datasets.