This study used the finite element method to investigate the acoustic bandgap (ABG) characteristics of three-dimensional pentamode metamaterial (PM) structures under the thermal environment, and a method for controlling the PM ABG based on external temperature variation is also proposed. The results indicate that the complete acoustic bandgap can be obtained for a PM in the thermal environment, which makes the PM combine the bandgap characteristics of phononic crystals. More than that, the bandwidth and locations of ABGs can be effectively manipulated by controlling the temperature. Considering the softening effect of thermal stresses, the ABG gradually moves to lower frequencies as the temperature increases. Based on this, different degrees of ABG tunability can be achieved by changing the thermal environment to propagate or suppress acoustic waves of different frequencies. This work provides the possibility for PMs to realize intelligent regulation of the bandgap.

Accurate prediction of student graduation status is crucial for higher education institutions to implement timely interventions and improve student success. While existing methods often rely on single data sources or generic model architectures, this paper proposes a novel Multi-Branch Convolutional Neural Network (MBCNN) that systematically integrates multi-dimensional factors influencing student outcomes. The model employs eight dedicated branches to capture both subjective and objective features from four key dimensions: student characteristics, school resources, family environment, and societal factors. Through robust normalization and hierarchical feature fusion, MBCNN effectively learns discriminative representations from these heterogeneous data sources. Evaluated on a real-world dataset from Polytechnic Institute of Portalegre, our approach demonstrates superior performance compared to traditional and up-to-date machine learning methods, achieving improvements of 4.07–17.35% in accuracy, 4.60–20.19% in weighted precision, 4.07–17.35% in weighted recall, and 4.59–18.73% in weighted F1-score. The results validate that domain-specific neural architectures, designed to align with the inherent structure of educational data, significantly enhance prediction accuracy and generalization capability.

The cultivation of high-quality talents relies on the synergistic interaction of various educational stakeholders, including schools, families, and society, within the educational system. With the rapid advancement of artificial intelligence (AI) technology, new opportunities have emerged for constructing and optimizing collaborative education mechanisms. Based on a feature-rich and large-scale real dataset, this paper conducts a case study to explore novel approaches for leveraging AI to empower a cooperative education system. Specifically, correlation and association analysis methods from traditional statistics are first employed to quantify pairwise feature relationships, providing a basis for identifying key factors influencing student development. Subsequently, principal component analysis (PCA) is applied to extract dominant components from the dataset, assess the intrinsic information carried by each feature, and uncover latent relationships among features. Finally, leveraging the multi-source and heterogeneous nature of the cooperative education system, a novel multi-branch neural network model (MBDNN) is proposed to achieve accurate prediction of student academic performance. This study can provide reference and methodological support for effectiveness evaluation and decision-making within the cooperative education system.