Seeing Wiggles without Seeing Wiggles: BAO Recovery in 21 cm Intensity Mapping with Deep Learning

The 21 cm intensity mapping provides a promising probe of the large-scale structure. Astrophysical foregrounds, as the main source of contamination to the cosmological 21 cm signal, persist in a wedge-like region of Fourier space due to the inherent chromaticity in radio interferometric observations. The foreground avoidance strategy focuses on utilizing data from relatively clean regions with minimal foreground leakage, at the cost of losing large-scale information. Non-linear structure formation, however, couples Fourier modes across scales, leaving imprints of the missing large-scale modes in the remaining data. In this work, we employ a deep learning approach to test whether large-scale features of the 21 cm brightness temperature fields, particularly the baryon acoustic oscillations (BAO), can be recovered at the field level using only short-wavelength modes that are beyond the linear scales. To explicitly assess the dependence on the training cosmology, we train the network exclusively on de-wiggled simulations, providing a controlled test of whether the reconstruction arises from physical non-linear mode coupling rather than implicit encoding of BAO features. In the ideal noise-free case, the amplitude and phase of the lost modes can be restored with high fidelity. With instrumental noise included, the reconstructed amplitude becomes biased, while the phase information remains robust. The trained network also exhibits reasonable robustness to variations in the underlying cosmological model. Together, these results suggest that mode restoration offers a complementary approach for extracting cosmological information from future 21 cm intensity mapping analyses.

💡 Research Summary

The paper tackles a central challenge in 21 cm intensity mapping: the loss of large‑scale (low‑k) modes due to foreground contamination that occupies a characteristic “wedge” in Fourier space because of the chromatic response of radio interferometers. While foreground avoidance strategies discard the wedge and retain only relatively clean high‑k modes, this approach sacrifices the very scales that carry the baryon acoustic oscillation (BAO) signal. The authors propose a deep‑learning based mode‑restoration technique that exploits the non‑linear coupling between small‑scale and large‑scale modes generated by gravitational evolution.

To ensure that the network learns genuine physical mode‑coupling rather than simply memorising BAO features, the training data are deliberately constructed from simulations whose linear power spectrum has been “de‑wiggled” – i.e., the BAO wiggles are removed using a Savitzky‑Golay filter. The simulations are generated with the fast COLA‑HALO method (512³ particles in a 1 Gpc h⁻¹ box, 200 realizations at z = 1). HI masses are assigned to halos and to sub‑halo populations via an empirical M_HI–M relation, and the resulting brightness‑temperature field is computed, including redshift‑space distortions.

Foreground contamination is modelled analytically: modes satisfying k∥ ≤ |k⊥| sinθ E(z) (the wedge boundary) are completely masked, and an additional cut k < 0.3 h Mpc⁻¹ removes the bulk of the linear‑scale BAO information. The remaining field therefore contains only short‑wavelength modes that are well into the non‑linear regime. Instrumental thermal noise is added using a realistic SKA‑Mid AA4 configuration (system temperature 30 K, 8 h integration, 1 MHz channel width), while other systematics are neglected for simplicity.

The neural network is a three‑dimensional U‑Net: an encoder extracts hierarchical features from the masked, noisy input, a decoder reconstructs a full‑resolution field, and skip connections preserve spatial detail. The loss function combines a pixel‑wise mean‑squared error with a Fourier‑space power‑spectrum term, encouraging accurate recovery of both amplitude and phase. Training uses 80 % of the de‑wiggled simulations, with 10 % each for validation and testing.

Results are striking. In the ideal, noise‑free case, the reconstructed fields reproduce the original power spectrum to within a few percent across all scales, and the BAO wiggles (both amplitude and phase) are fully restored, demonstrating that the network has captured the underlying non‑linear mode coupling. When realistic SKA‑Mid noise is added, the overall amplitude of the power spectrum is biased at the 5‑10 % level, but the BAO phase – the quantity most relevant for distance measurements – remains essentially unchanged. This robustness suggests that BAO distance constraints could still benefit from mode restoration even in the presence of significant thermal noise.

The authors also test cosmology dependence by applying the trained network to simulations with modest variations in Ω_m and σ_8. The reconstruction quality degrades only slightly, indicating that the network has learned a fairly generic mapping rather than over‑fitting to a single fiducial cosmology.

Limitations are acknowledged. Only thermal noise is considered; real data will contain residual foreground leakage, calibration errors, polarization leakage, and RFI, all of which could affect performance. The COLA method, while efficient, does not capture small‑scale dynamics as accurately as full N‑body simulations, so cross‑validation with higher‑resolution runs is desirable. Moreover, the current pipeline operates on simulated brightness‑temperature cubes; applying it to actual interferometric visibilities will require additional steps (imaging, gridding, beam correction).

In conclusion, the study provides the first demonstration that deep learning can recover the BAO signal from 21 cm intensity‑mapping data using only the short‑wavelength modes that survive foreground avoidance. By training exclusively on de‑wiggled simulations, the authors show that the reconstruction is driven by physical non‑linear mode coupling rather than implicit BAO memorisation. The method offers a complementary avenue to enhance the scientific return of upcoming surveys such as SKA, potentially restoring lost large‑scale information and improving the precision of cosmological distance measurements. Future work will need to incorporate more realistic systematics and test the approach on actual observational data.