Constraining Dark Energy Dynamics in Curved Spacetime with Current Observations

We investigate a dark energy (DE) equation of state (EoS) parametrization in a curved spacetime using current observations. We constrain the model parameters by using observational Hubble data from Cosmic Chronometer (CC), Pantheon Plus SH0ES (PPS), and DESI BAO DR2, along with their reconstructed datasets using an Artificial Neural Network (ANN). The parameter $\alpha$ is constrained as $\alpha \approx 0.35 (\approx 0.56)$ from original (reconstructed) data. This means reconstruction pushes the model toward a significant deviation from the standard $\Lambda$CDM framework. We find that the curvature parameter $\Omega_{k0} = 0.068 \pm 0.029$ at 68\% CL with original data, suggests a slightly open universe, whereas with the reconstruction method, $\Omega_{k0} = -0.131 \pm 0.032$ at 68\% CL suggests a closed universe. This shift in the mean value indicates that the reconstruction method is highly sensitive to curvature. We perform statistical model comparison criteria, namely, AIC and BIC to assess the reliability of our framework.