Accurate determination of the optical properties of ultra-thin dielectric films is an essential and challenging task in optical fiber sensor systems. However, nanoscale thickness identification of these films may be laborious due to insufficient and protracted classical curve matching algorithms. Therefore, this experimental study presents an application of a radial basis function neural network in phase diffraction-based optical characterization systems to determine the thickness of nanoscale polymer films. The non-stationary measurement data with environmental and detector noise were subjected to a detailed analysis. The outcomes of this investigation are benchmarked against the linear discriminant analysis method and further verified by means of scanning electron microscopy. The results show that the neural network has reached a remarkable accuracy of 98% and 82.5%, respectively, in tests with simulation and experimental data. In this way, rapid and precise thickness estimation may be realized within the tolerance range of 25 nm, offering a significant improvement over conventional measurement techniques.