This work presents a novel methodology for the development of refined structural theories for the modal analysis of sandwich composites. Such a methodology combines three well-established techniques, namely, the Carrera Unified Formulation (CUF), the Axiomatic/Asymptotic Method (AAM), and Artificial Neural Networks (NN). CUF generates structural theories and finite element arrays hierarchically. CUF provides the training set for the NN in which the structural theories are inputs and the natural frequencies targets. AAM evaluates the influence of each generalized displacement variable, and NN provides Best Theory Diagrams (BTD), i.e., curves providing the minimum number of nodal degrees of freedom required to satisfy a given accuracy requirement. The aim is to build BTD with far less computational cost than in previous works. The numerical results consider sandwich spherical shells with soft cores and different features, such as thickness and curvature to investigate their influence on the choice of generalized displacement variables. The numerical results show the importance of third-order generalized displacement variables and prove that the present framework can be of interest to evaluate the performance of any structural theory as typical design parameters change and provide guidelines to the analysts on the most convenient computational model to save computational cost without accuracy penalties.