## 6 Discussion  
Up to now, the surrogate model using a neural network for a finite element model has been focused on a single component, for which all the elements are connected homogeneously. In this study, the GCN-CNN network was proposed to predict panel-vibration-induced structure-borne noise in a cavity by combining the responses from each sub-system to predict the full-system response.  
The GCN was used to predict the natural frequency of the morphed panel and various shape of the cavity, which are the finite element model. The prediction accuracy of the panel and cavity was 0.956 and 0.974 r-square values, respectively.  
To predict the vibration and acoustic response up to 500 Hz in the 1/12 octave band, a triangular-shaped inference function, for which the peak frequencies are based on the predicted frequency using the GCN, was adopted. This is an efficient way to predict the frequency response using a small number of datasets, and it achieves the r-square value 0.912 for the panel and 0.914 for the cavity.  
The 2D-CNN was used to represent the coupling effect between the panel and cavity to predict structure-borne noise in a cavity. Using this proposed method, an 0.858 average r-square value was achieved.  
In this study, the graph classification method for the GCN was adopted to predict the natural frequency, and then the knowledge-based inference function was used to predict  
Figure 15: Panel–cavity coupled interior noise prediction—Step 3. Blue—target; red—predicted.  
the components average response. This is a novel approach considering the limited number of datasets in a real engineering problem and how the size of the data can be reduced for the loss function. Table 1 summarizes the proposed method, predictions, and the achieved r-square values at each step.  
Another proposed option is to predict the frequency response directly because the graph classification method aggregates the node embeddings into a single embedding using the global mean in a readout layer, where the single embedding is the target.  
A potential further research direction could be adding a node classification method for the GCN to learn the mode shape depending on the changes in the panel and cavity shape, which could lead to a direct prediction of frequency response using the GCN. The graph classification method which was used in this study aggregates the node embeddings into a single embedding using the global mean in a readout layer, so it is unclear whether the trained individual features of the node reflect the actual panel behavior. To predict the frequency response, each mode shape should be predicted because the panel radiation efficiency depends on the mode shape. Adding a node classification to the selected node could be an efficient way. But there is a need to find a balance between the amount of data to compare for the loss function and the prediction accuracy.  
This study is the first step towards creating a surrogate model of an engineering system with various sub-systems by changing it into a heterogeneous graph. A graph network for more diverse sub-system combinations and connection methods will be developed in future.  
Conceptualization, S.-Y.L. and S.-K.L.; methodology, S.-Y.L.; software, S.-Y.L.; validation, S.-Y.L. and S.-K.L.; formal analysis, S.-Y.L.; investigation, S.-K.L.; resources, S.-Y.L.; data curation, S.-Y.L.; writing--original draft preparation, S.-Y.L.; writing--review and editing, S.-K.L. and S.-Y.L.; visualization, S.-Y.L.; supervision, S.-K.L.; project administration, S.-K.L.; funding acquisition, S.-K.L. All authors have read and agreed to the published version of the manuscript. This work was supported by the INHA UNIVERSITY Research Grant.  
The authors declare no conflict of interest.