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The use of Gaussian Process Regression (GPR) for foregrounds mitigation in data collected by the LOw-Frequency ARray (LOFAR) to measure the high-redshift 21-cm signal power spectrum has been shown to have issues of signal loss when the 21-cm signal covariance is misestimated. To address this problem, we have recently introduced covariance kernels obtained by using a Machine Learning based Variational Auto-Encoder (VAE) algorithm in combination with simulations of the 21-cm signal. In this work, we apply this framework to 141 h (⁠|${\approx} 10$| nights) of LOFAR data at |$z \approx 9.1$|⁠ , and report revised upper limits of the 21-cm signal power spectrum. Overall, we agree with past results reporting a 2- |$\sigma$| upper limit of |$\Delta ^2_{21} \ \lt\ (80)^2~\rm mK^2$| at |$k = 0.075~h~\rm Mpc^{-1}$|⁠. Further, the VAE-based kernel has a smaller correlation with the systematic excess noise, and the overall GPR-based approach is shown to be a good model for the data. Assuming an accurate bias correction for the excess noise, we report a 2- |$\sigma$| upper limit of |$\Delta ^2_{21} \ \lt\ (25)^2~\rm mK^2$| at |$k = 0.075~h~\rm Mpc^{-1}$|⁠. However, we still caution to take the more conservative approach to jointly report the upper limits of the excess noise and the 21-cm signal components. [ABSTRACT FROM AUTHOR]

The 21-cm line emitted by neutral hydrogen is the most promising probe of the Epoch of Reionization (EoR). Multiple radio interferometric instruments are on the cusp of detecting its power spectrum. It is therefore essential to deliver robust theoretical predictions, enabling sound inference of the coeval Universe properties. The nature of this signal traditionally required the modelling of |$\mathcal {O}(10^{7-8} \, {\rm Mpc}^3)$| volumes to suppress the impact of cosmic variance. However, the recently proposed Fixed & Paired (F&P) approach uses carefully crafted simulation pairs to achieve equal results in smaller volumes. In this work, we thoroughly test the applicability of and improvement granted by this technique to different observables of the 21-cm signal from the EoR. We employ radiation-magneto-hydrodynamics simulations to ensure the most realistic physical description of this epoch, greatly improving over previous studies using a seminumerical approach without accurate galaxy formation physics and radiative transfer. We estimate the statistical improvement granted by the F&P technique on predictions of the skewness, power spectrum, bispectrum, and ionized regions size distribution of the 21-cm signal at redshift 7 ≤ z ≤ 10 (corresponding to |${\ge}80{{\ \rm per\ cent}}$| of the gas being neutral). We find that the effective volume of F&P simulations is at least 3.5 times larger than traditional simulations. This directly translates into an equal improvement in the computational cost (in terms of time and memory). Finally, we confirm that a combination of different observables like skewness, power spectrum, and bispectrum across different redshifts can be utilized to maximize the improvement. [ABSTRACT FROM AUTHOR]

In recent years, a Gaussian process regression (GPR)-based framework has been developed for foreground mitigation from data collected by the LOw-Frequency ARray (LOFAR), to measure the 21-cm signal power spectrum from the Epoch of Reionization (EoR) and cosmic dawn. However, it has been noted that through this method there can be a significant amount of signal loss if the EoR signal covariance is misestimated. To obtain better covariance models, we propose to use a kernel trained on the grizzly simulations using a Variational Auto-Encoder (VAE)-based algorithm. In this work, we explore the abilities of this machine learning-based kernel (VAE kernel) used with GPR, by testing it on mock signals from a variety of simulations, exploring noise levels corresponding to ≈10 nights (≈141 h) and ≈100 nights (≈1410 h) of observations with LOFAR. Our work suggests the possibility of successful extraction of the 21-cm signal within 2σ uncertainty in most cases using the VAE kernel, with better recovery of both shape and power than with previously used covariance models. We also explore the role of the excess noise component identified in past applications of GPR and additionally analyse the possibility of redshift dependence on the performance of the VAE kernel. The latter allows us to prepare for future LOFAR observations at a range of redshifts, as well as compare with results from other telescopes. [ABSTRACT FROM AUTHOR]