Neural network reconstruction of H'(z) and its application in teleparallel gravity

In this work, we explore the possibility of using artificial neural networks to impose constraints on teleparallel gravity and its $f(T)$ extensions. We use available Hubble parameter observations from cosmic chronometers baryon acoustic oscillations different galaxy surveys. discuss procedure for training a network model reconstruct diagram. Further, describe obtain $H'(z)$, first order derivative $H(z)$, which is novel approach method reconstruction. These analyses are complemented with further studies impact two priors put $H_0$ assess their analysis, local measurements by SH0ES team ($H_0^{\text{R20}} = 73.2 \pm 1.3$ km Mpc$^{-1}$ s$^{-1}$) updated TRGB calibration Carnegie Supernova Project ($H_0^{\text{TRGB}} 69.8 1.9$ s$^{-1}$), respectively. Additionally, investigate validity concordance model, through some cosmological null tests these reconstructed data sets. Finally, allowed functions combinations observational Results show that $\Lambda$CDM lies comfortably included at 1$\sigma$ confidence level all examined cases.