## 4 Neural Network Architectures and Implementation  
In this study, three multi-input, multi-output (MIMO) models were constructed with six process parameters, melt temperature, mold temperature, injection speed, packing pressure, packing time, and cooling time, as input parameters, and the mass, diameter, and height of the molded product as output parameters. One of the models is Network A, shown in Figure 8, a conventional artificial neural network (ANN) that combines all three output parameters in a single-task layer. The other two models were built using multi-task learning by grouping the output parameters based on their physical meanings and characteristics. One model groups length, represented by diameter and height, and separates mass as a separate group, as shown in Network B (Figure 9), while the other model, Network C, classifies all output parameters into separate groups, as shown in Figure 10.  
Figure 8: Network A with the output parameters of mass, diameter, and diameter being connected to the single-task layer.  
Figure 9: Network B with diameter and height as one group and mass as the other group.  
Table 2 shows the hyperparameters used to build the ANN models in this study and the search ranges for optimization. In this study, the exploration of optimizing hyperparameters included the seed number. Typically, in the construction of artificial neural networks, the seed number is set to a specific value while the remaining hyperparameters are explored. However, the seed number, akin to the batch size, possesses algorithmic characteristics within the device and program that trains the neural network, and is a factor that must be carefully considered. In the initial stages of the research, the seed number was fixed to a specific value without exploration. However, it was observed that, even with the same structure of artificial neural networks, the results could vary significantly depending on the seed number. Therefore, in this study, to prevent such variations and optimize results, the seed number was treated as a hyperparameter and explored for optimal values. The optimizer was consistently set to the widely used Adams optimizer, with its parameters defined based on the research proposed by [PERSON] et al. [15]. Initially, an artificial neural network was constructed by applying the widely used default coefficient values to the Adams optimizer. However, confirming variations in the performance of the Adams optimizer observed in previous studies and recognizing the need for coefficient exploration depending on the dataset, this research applied the coefficient ranges used in exploration in the study by [PERSON] et al. [15]. This approach aimed to search for and apply the optimal coefficients in the Adams optimizer. The activation function was set to the popular ELU function from the ReLU family, and the initializer was chosen as the He normal initializer, which is known for its good performance along with that of the ReLU family. For the output layer, where the results of the neural network model are produced, a linear function was applied as the activation function, and the Xavier normal initializer, which performs well with the linear function, was used. Other hyperparameters were explored according to the ranges shown in Table 2. However, to facilitate a comparison of the performance of Networks A, B, and C, the number of common hidden layers was set to 3, and the number of hidden layers associated with each output parameter was set to 1. In addition, the root mean square errors (RMSEs) were used as a metric to evaluate the performance during the training process of the ANNs.  
Figure 10: Network C with mass, diameter, and height all categorized into separate groups.