https://doi.org/10.1140/epjp/s13360-025-06114-5
Regular Article
Prediction and inverse design of bandgaps in acoustic metamaterials using deep learning and metaheuristic optimization techniques
School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran
Received:
5
October
2024
Accepted:
10
February
2025
Published online:
11
March
2025
Obtaining the dispersion curves of phononic crystals and acoustic metamaterials is a costly and complex process. Their inverse design possesses even greater challenges. In this work, to handle these issues more efficiently, we apply machine learning methods including random forests, extra trees, k-nearest neighbors, and artificial neural networks to predict dispersion bandgaps in cylindrically pillared acoustic metamaterials. We consider three main design parameters including the ratios of the substrate layer thickness, cylinder diameter, and cylinder height to the length of the unit cell. After tuning the hyperparameters of models and training them, the best-trained model was obtained from deep learning (multi-layer artificial neural networks) with a determination coefficient 
of 0.997. Furthermore, we employ the trained models for the inverse design of the cylindrically pillared phononic crystals with four different bandgap ratios as objectives, successfully. The developed artificial neural network demonstrates the greatest performance, achieving an 
of 0.998. Then, we develop an application (a graphical user interface) using the trained model to predict and inverse design of the metamaterials for the desired bandgap ratios. To interpret the trained model better, we present Shapley values, which provide a detailed understanding of how each geometric parameter influences the predicted bandgap ratios.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
