Although artificial neural networks (ANNs) are powerful tools in terms of their high posttraining computational speed and their flexibility to construct complex nonlinear mappings from relatively few known data samples, a survey of past applications of ANNs to the area of core parameter prediction reveals drawbacks such as low prediction accuracy, lack of robust generalization, large network dimensionality, and typically high training requirements. This study provides a brief survey of past and recent applications of ANNs to direct core parameter predictions as well as an alternate hybrid approach that avoids the aforementioned shortcomings of ANNs by combining the mathematical rigor of generalized perturbation theory along with the strong qualities of ANNs in error prediction situations. The results presented focus exclusively on the neutron diffusion's fundamental mode eigenvalue (i.e., 1/keff) and demonstrate the viability of computationally inexpensive adaptive ANN error controllers for perturbation theory applications.