## 1 Introduction  
Deep learning has been adopted and showed remarkable results in various areas, like object detection and recognition, natural language processing, healthcare and medical applications, self-driving cars, and so on [1]. The commonality of these fields is to simulate human cognitive ability, which is generally a difficult field to solve in a theoretical way. Nowadays, deep learning has begun to be applied to the field of finding solutions, where it has been used as analytical formulas and achieved considerable results. A typical example is physics-informed machine learning [2], while research on building a surrogate model using deep learning and a graph neural network is also actively underway [3; 4; 5]. A conventional surrogate model requires that all training data should have the same parameterization. And, if the model used for prediction has a different parameter than the pre-trained surrogate model, there is a disadvantage that the pre-trained surrogate model could not be applied to other models which have different parameters. A surrogate model using deep learning can overcome this obstacle. Building a surrogate model using deep learning has been mainly focused on the parameterized model, for which the system can be represented by moderate amounts of parameters. For example, machine learning algorithms proposed to estimate the time-varying response of a one-dimensional beam [6] and graph-based surrogate model were proposed for trusses [7] to predict the displacement field from static loads given the structure's geometry as an input and also explore transfer learning within the context of engineering design. But the physics model built for engineering applications generally uses the finite element method (FEM) which has numerous parameters like nodes which have location information and connections to represent the complicated structure's shape. To learn the parameter of this complicated model shape, graph neural networks (GNNs) [8; 9] are the most promising because they can learn in non-Euclidian space and have node-invariant characteristics. Among GNNs, graph convolutional networks (GCNs) [10] were selected for use in this study as a surrogate model of mesh-based structure-borne noise analysis because they can explicitly take into account the connectivity patterns between nodes when performing the convolution operation. FEM has been used for various engineering applications and also for structure-borne noise analysis. It has numerous numbers of nodes and meshes to represent the structure's geometry in a non-Euclidian space. An Euclidian-space-based method like a CNN (convolutional neural network) [11] and PointNet [12] has a limitation in terms of the irregular location of each of the nodes of the FEM, but the GNN holds a strength in this area. Surrogate model building using the GNN is an emerging area, and the application of the engineering problem is expanding nowadays [13]. Another main focus of this study is the application of the GCN-based surrogate model to the system, for which several sub-systems are combined. Like a vehicle model, it consists of a lot of sub-systems, and they are combined to make up a total system. Up to now, building a surrogate model for a finite element model has been focused on the single component to which all elements are connected homogeneously, and the excitation and response location which is within the same system [3; 13]. However, in engineering problems, several components are connected with various kinds of connection like a spring, bolt, coupling structure with an interior cavity, and so on. This study proposes a GCN-CNN architecture for building a surrogate model for a panel-cavity coupled system response by combining each sub-system response. The concept of building a surrogate model of each sub-system and then combining to the total system is an effective way to predict the total system response of various sub-system combinations. In this study, irregular shape panels were generated using morphing and predicting natural frequencies using the GCN.