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In the context of the discrepancies between the early and late universe, weemphasize the importance of independent measurements of the cosmic curvature inthe late universe. We present an investigation of the model-independentmeasurement of the cosmic curvature parameter $\Omega_k$ in the late universewith the latest Hubble parameter $H(z)$ measurements and type Ia supernovae(SNe Ia) data. For that, we use two reconstruction methods, the Gaussianprocess (GP) and artificial neural network (ANN) methods, to achieve thedistance construction from $H(z)$ data. Our analysis reveals that the GP methodprovides the most precise constraint on $\Omega_k$, with a constraint precisionof $\xi(\Omega_k)=0.13$, surpassing recent estimations using similar methods.The GP method consistently indicates a preference for a flat universe at the2$\sigma$ confidence level. Moreover, we find that the choice of reconstructionmethod influences the estimation of $\Omega_k$. The ANN reconstruction methodexhibits higher sensitivity to the addition of BAO $H(z)$ data, resulting incomparable constraint precision to the GP method. A discrepancy exists betweenthe best-fit values obtained by these two reconstruction methods, indicatingtheir dependence on the reconstruction approach. However, we anticipate thatwith the improvement of sample size and precision of observational $H(z)$ data,the estimation of $\Omega_k$ using this approach will become more robust andreliable.

Model-independent measurement of cosmic curvature with the latest $H(z)$ and SNe Ia data: A comprehensive investigation