Uncertainty-aware prediction of mechanical properties in graphene using random forest and Monte Carlo simulations

Accurate prediction of graphene’s mechanical properties is essential for its application in advanced technologies, but traditional molecular dynamics (MD) simulations require prohibitive computational resources for comprehensive parametric studies. While statistical measures such as variance can be extracted directly from MD trajectories at fixed simulation conditions, extending such uncertainty analysis across a multi-parameter design space would require thousands of independent simulations, making it computationally infeasible. This study presents a surrogate modeling framework that integrates Random Forest (RF) regression with Monte Carlo (MC) sampling to enable rapid propagation of input uncertainties across the full design space — a capability that MD simulation alone cannot provide efficiently. Using a dataset of 75 points generated from MD simulations, the RF surrogate learns the mechanical response surface of graphene as a function of aspect ratio, temperature, number of atomic planes, and vacancy defect concentration for both armchair and zigzag configurations. Once trained, the RF–MC framework propagates realistic input uncertainties — arising from fabrication tolerances, thermal fluctuations, and defect variability — through the surrogate in milliseconds, yielding predictive distributions and 95% confidence intervals for Young’s modulus and shear modulus across thousands of design configurations. The model achieves R2 scores of 0.95-−0.99 across all properties with RMSE of 0.002-−0.022 TPa, comparable to experimental measurement uncertainties. Compared to the earlier multi-gene genetic programming approach applied to the same dataset, the RF–MC framework improves prediction accuracy while adding uncertainty quantification that was previously absent. The results confirm distinct anisotropic behavior between armchair and zigzag orientations, with zigzag configurations exhibiting more consistent mechanical behavior, lower Young’s modulus, and higher shear modulus. By reducing computation time from weeks to seconds while enabling design-space-wide uncertainty propagation, this framework offers a practical tool for reliability-aware graphene materials design.