As operational reactors age, they experience increased mechanical vibrations, particularly affecting the in-core sensors and complicating the reconstruction of neutronic fields. Traditional field reconstruction methods are inadequate for dealing with the spatial movement of sensors. To address this, a novel technique combining Voronoi tessellation with convolutional neural networks (V-CNN) has been proposed. This method projects observations from movable sensors onto a unified global field structure through Voronoi tessellation, which preserves sensor magnitude and location data. The V-CNN learns the mapping from these observations to the global field, capable of reconstructing multi-physics fields such as fast flux, thermal flux, and power rate from single-field observations like thermal flux. Numerical tests using the IAEA benchmark have shown its effectiveness, achieving average relative errors below 5\% and 10\% in $L_2$ norm and $L_{\infty}$ norms, respectively, within a 5 cm amplitude around nominal sensor locations. Furthermore, the challenge of balancing lightweight design with the ability to handle unstructured data and robustness against observation noise and sensor vibrations is tackled by the introduction of the EIM-NN algorithm. This algorithm employs neural networks to determine coefficients within the subspace identified by the EIM algorithm. An enhanced version, the EIM-TNN algorithm, incorporates Tikhonov regularization into the loss function to improve robustness. The neural network, consisting of only two fully connected layers, is adept at managing unstructured data while maintaining a compact structure. The experimental results highlight the algorithm`s robustness against noise and vibrations, without sacrificing the accuracy of the original data fit. Its lightweight nature ensures that the additional training time and memory requirements are minimal compared to EIM, making it suitable for various industrial applications.