## 1 Introduction  
Injection molding is the process of injecting molten resin at high temperatures into a cavity in a mold at high speeds and pressures to form the final product. This process involves a complex interplay of various physical phenomena and material behaviors, such as rheology, flow dynamics, and heat transfer, at each stage of the process. Consequently, research has been actively pursued for many years to model the relationships between influencing factors such as process conditions in the injection molding process and the quality of the molded product, with the goal of predicting the process and optimizing product quality [1, 2]. In recent years, with the advent of the Fourth Industrial Revolution, artificial intelligence (AI) technology has found applications in various fields such as data mining, image processing, engineering system modeling, technical control, and more. This integration has been made possible via the development of intelligent information technology and data computing, ushering in a new era of AI-driven solutions. Among them, there is a growing industrial demand for artificial neural networks (ANNs), which have shown strong performance in unraveling complex nonlinear relationships, making them one of the most promising languages in the field of artificial intelligence [3, 4]. In line with this paradigm shift, the injection molding industry has also embraced the application of artificial intelligence technology to overcome the limitations of existing techniques for predicting the relationship between process factors and product quality in injection molding processes. Models for predicting the quality of molded products using ANNs can be categorized into two types. One is the multi-input, single-output (MISO) structure, which predicts a single quality parameter for multiple process conditions, while the other is the multi-input, multi-output (MIMO) structure, which predicts multiple quality parameters for different process conditions. [PERSON] et al. [5] conducted a study in which they used a MISO-ANN to predict the mass of injection-molded products based on 10 process conditions, including melt temperature and mold temperature, set as input parameters. Their research aimed to explore the optimal conditions for molding products with the desired mass. The performance evaluation of the established ANN showed that the deviation between the predicted values and the actual values of the mass was within 0.23 \(\pm\) 0.02 g. Based on this, they used the ANN to derive the process for a product with a target mass of 41.14 g. Injection molding experiments were conducted, and when the mass of the product was compared with the target mass, it showed a minimal deviation of 0.15 \(\pm\) 0.07 g. This demonstrated a high degree of accuracy in deriving process conditions. They concluded that the ANN model for this product had a high degree of accuracy and reliability. [PERSON] et al. [6] used 2 mm thick flat samples and used simulations to create a dataset with three output variables: product mass, length, and width. This dataset was based on six input variables including resin temperature, mold temperature, injection time, packing pressure level and time, and cooling time. Various experimental designs were used to construct the dataset. When comparing the prediction accuracy of ANNs for datasets generated using different experimental designs, the central composite design (CCD) showed the highest coefficient of determination at 0.930, indicating the most effective performance. However, in some cases, the D-optimal design and the L25 orthogonal array method also showed coefficients of determination similar to those of the CCD, indicating excellent performance. This indicates that ANNs can achieve a high level of accuracy and reliability and produce good results. However, in the case of MIMO models, multiple quality factors with different physical meanings and characteristics are evaluated using a single feed-forward neural network.