Data-driven inverse design of graphene Kirigami with negative Poisson's ratio using machine learning and genetic algorithms

Graphene's mechanical properties, particularly its Poisson's ratio, can be tuned by introducing structural defects like perforations, which enhances its potential for flexible nanoelectronics. We propose a framework that integrates machine learning (ML) with genetic algorithms (GA) to efficiently predict and inversely design rectangular perforated graphene Kirigami structures. The approach specifically targets configurations exhibiting a negative Poisson's ratio (NPR). Unlike conventional rotating rigid-unit systems, the NPR effect in this case results from the combined influence of in-plane rotation and out-of-plane deformation. Molecular dynamics (MD) simulations were performed to generate a dataset of Poisson's ratios for graphene Kirigami structures with varying perforation geometries. Four machine learning models, including Multilayer Perceptron (MLP), k-Nearest Neighbors (KNN), Support Vector Regression (SVR), and Extreme Gradient Boosting (XGBoost), were trained to predict Poisson's ratios. XGBoost exhibited superior accuracy and generalization. Feature importance analysis revealed that perforation interspacing (IS) strongly influences Poisson’s ratio, whereas perforation aspect ratio (AR) and unit length (L) exert weaker effects. The optimized XGBoost model was integrated with a GA for inverse design, successfully generating graphene Kirigami configurations with targeted negative Poisson's ratios. The ML-GA framework was validated through MD simulations, showcasing its effectiveness in tackling complex material design challenges. This work highlights the potential of integrating machine learning and genetic algorithms for efficiently optimizing graphene and other advanced materials.