Physics-Informed Neural Networks for Real-Time Metamaterial Design: Predicting Band Gap Properties from 2D Elastic Structures with Domain Knowledge Injection

Accurate prediction of band gap properties in 2D elastic metamaterials is a time-consuming process that hinders real-time design optimization. This study presents the first comprehensive machine learning framework solely developed for the prediction of band gap location and width in 2D elastic metamaterial structures using physics-informed approaches. We compare four machine learning approaches - Random Forest, XGBoost, Gradient Boosting, and Stacking Regressor - on a dataset of 1, 400 unique metamaterial structures defined as binary 7×7 grid geometries. Our proposed stacking ensemble approach achieves R² scores of 0.744 for band gap location prediction and 0.641 for band gap width prediction, representing a significant advance for metamaterial-specific problems within the constraints of current geometric-only datasets. Cross-validation supports the stability of our approach with mean R² values of 0.629±0.084 for the stacking regressor. Feature importance analysis provides the critical design parameters governing band gap formation, providing physical insight for metamaterials design. The developed framework enables the rapid screening of metamaterial geometries for target acoustic applications, reducing design times from hours to milliseconds and enabling real-time optimization procedures.