A neutron noise-based technique for the localization of excessively vibrating control rods is elaborated upon in the previous three papers of this series. The method is based on the inversion of a formula that expresses the auto- and cross spectra of three neutron detector signals through the parameters of the vibrating rod, i.e., equilibrium position and displacement components. Successful tests of the algorithm with both simulated and real data were reported in the previous papers. The algorithm had nevertheless certain drawbacks, namely, that its use requires expert knowledge, the redundancy of extra detectors cannot be utilized, and with realistic transfer functions the calculations are rather lengthy. The use of neural networks offers an alternative way of performing the inversion procedure. This possibility was investigated by constructing a network that was trained to determine the rod position from the detector spectra. It was found that all shortcomings of the traditional localization method can be eliminated. The neural network-based identification was also tested with success.