In this paper, an efficient methodology to obtain Best Theory Diagrams (BTDs) for composite and sandwich plates is presented. A BTD is a curve that provides the minimum number of unknown variables in a kinematic theory for the desired accuracy. The present work combines genetic algorithms (GAs) and neural networks (NNs) to construct BTDs efficiently, faster than using GAs alone. A structural finite element model of a plate is derived using the principle of virtual displacements. Arbitrary plate models are considered in a compact manner using Carrera Unified Formulation. As reported in previous papers by the authors, a multiobjective optimization technique using a GA is applied to build BTDs for a given structural problem. The plate models stresses and displacements are compared to those of a reference solution, and a plate model performance is quantified in terms of the number of unknown variables, the mean error and standard deviation of the stresses and displacements. As a novelty, a NN is trained to reproduce the mean error and standard deviation of the stresses and displacements for any plate model refined from a reference plate model. In this way, the computational time required to build BTDs using the finite element method is optimized. BTDs for different boundary conditions not previously investigated are reported in this paper. The results of the present method are compared to those obtained via GA using the finite element solution. The BTDs build using a NN are comparable to those obtained by a regular finite element analysis. Refined plate models with appropriate predictive capabilities and measured computational cost are presented. The results show that the NN reduces the computational time to build BTDs drastically.