Accelerated, Cost-Effective, and Accurate Prediction of Carbon Nanotube Stress–Strain Characteristics under Thermal Vibration

In this study, we propose an ensemble learning framework combining Random Forest, Gradient Boosting, and Extra Trees regressors to efficiently predict the full stress–strain response of carbon nanotubes (CNTs) with varying chirality and diameters up to 4 nm. The dataset comprises 816 CNT configurations generated through molecular dynamics simulations, with strain values incremented on average by 0.01%. A group-based splitting strategy ensures that CNTs with identical chirality indices are strictly separated between training and testing sets, thereby enforcing true generalization. The ensemble model achieves high predictive accuracy, with R2 exceeding 0.999, normalized RMSE below 0.005, and low mean absolute errors, while capturing subtle stress fluctuations due to thermal vibrations. Comparative analysis with existing machine learning approaches demonstrates that the proposed method provides accelerated, cost-effective, and robust predictions, reconstructing complete stress-strain curves and outperforming single-model approaches. This framework offers a practical tool for rapid and reliable assessment of CNT mechanical behavior, facilitating accelerated design and optimization of nanomaterial-based devices.