Evaluation of Best Structural Theories using Neural Networks and Adaptive Sampling

This work presents an Adaptive Sampling-based surrogate framework for predicting the accuracy of higher-order beam theories generated within the Carrera Unified Formulation. The objective is to identify the minimal set of generalized displacement variables required to achieve a prescribed accuracy, thereby reducing the need for exhaustive high-fidelity structural analyses. Structural theories are built using Taylor-like polynomial expansions, and an Adaptive Sampling strategy based on an Extra Trees Regressor iteratively selects the most informative generalized variables by combining predicted error, uncertainty, and structural diversity. The selected dataset is then used to train a Neural Network to predict the average error in natural frequencies. The proposed strategy is evaluated using Best Theory Diagrams, which relate model accuracy to the number of degrees of freedom. Results show that Adaptive Sampling achieves accuracy comparable to, and in some cases better than, random sampling at the same sampling budget, while correctly identifying the most effective structural theories with fewer high-fidelity analyses. The framework, therefore, provides an efficient tool for data-driven selection of refined beam models.