An investigation on ensemble machine learning algorithms for nonlinear stability response of a two-dimensional FG nanobeam

In this paper, the nonlinear buckling analysis of two-dimensional functionally graded nanobeams is investigated using ensemble machine learning (ML) techniques and semi-analytical approach based on Fourier series and Stokes’ transformation. Ensemble models such as XG boosting, gradient boosting, light gradient boosting, adaptive boosting, random forest, and extra trees regressor are utilized to explore the complex relationship between different input features and the buckling loads of the nanobeams. The training data for these models are derived from the nonlinear strain gradient theory. Performance of ML models are evaluated using multiple metrics such as R², MAE, MAPE, MSE and RMSE and visual representation techniques like Taylor plots, scatter plots, and box plots. Model interpretation using SHAP analysis is also employed for studying the impact and significance of each input feature on buckling loads. Among all the established models, light gradient boosting demonstrated superior performance in predicting the buckling loads accurately. It is shown that the ensemble ML models can accurately estimate the buckling loads of a two-dimensional functionally graded nanobeam with R² value of 0.999 given the adequate amount of training data.