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<p>The extraordinary wave manipulation properties of elastic metamaterials imply probable employment in vibration isolation, wave guiding, and sound control. However, their discovery and design remain problematic. Recent advancements in machine learning can accelerate this process by accurately predicting outcomes, such as bandgap behavior. While deep neural networks promise remarkable accuracy, they usually operate as black-box predictors and demand extensive training data. This paper proposes an interpretable and practical machine learning approach utilizing XGBoost, a gradient-boosted decision tree algorithm, to estimate the initial band gap position and bandwidth of 2D elastic metamaterials. XGBoost was selected for its efficiency, interpretability, and success with structured datasets, particularly ones of constrained size. The study utilizes a dataset of 10 × 10 binary-coded unit cell shapes and their accompanying band gap values. The proposed XGBoost model showed a mean absolute error (MAE) of 339.06 for band gap sites and 116.45 for bandwidth. The R<sup>2</sup> values were 0.1514 for locations and 0.062 for bandwidth. Despite moderate R<sup>2</sup> values, the model demonstrated increased performance in terms of error metrics compared to alternative approaches such as Random Forest, Support Vector Regression (SVR), k-Nearest Neighbors (k-NN), and Linear Regression. This framework offers a scalable technique to speed up metamaterial discovery and assist in the design of wave-control devices with appropriate geometries.</p>

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Machine learning-driven prediction of band gap characteristics in elastic metamaterials: an XGBoost-based approach

  • 期刊论文

  • 发表日期：

    2025年6月28日

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  • Kaifeng Chen,
  • Byung-Won Min,
  • Kunrong Zeng

摘要

The extraordinary wave manipulation properties of elastic metamaterials imply probable employment in vibration isolation, wave guiding, and sound control. However, their discovery and design remain problematic. Recent advancements in machine learning can accelerate this process by accurately predicting outcomes, such as bandgap behavior. While deep neural networks promise remarkable accuracy, they usually operate as black-box predictors and demand extensive training data. This paper proposes an interpretable and practical machine learning approach utilizing XGBoost, a gradient-boosted decision tree algorithm, to estimate the initial band gap position and bandwidth of 2D elastic metamaterials. XGBoost was selected for its efficiency, interpretability, and success with structured datasets, particularly ones of constrained size. The study utilizes a dataset of 10 × 10 binary-coded unit cell shapes and their accompanying band gap values. The proposed XGBoost model showed a mean absolute error (MAE) of 339.06 for band gap sites and 116.45 for bandwidth. The R2 values were 0.1514 for locations and 0.062 for bandwidth. Despite moderate R2 values, the model demonstrated increased performance in terms of error metrics compared to alternative approaches such as Random Forest, Support Vector Regression (SVR), k-Nearest Neighbors (k-NN), and Linear Regression. This framework offers a scalable technique to speed up metamaterial discovery and assist in the design of wave-control devices with appropriate geometries.