Injection molding is characterized by injecting a polymer melt into a cavity of a predefined geometry, where the material fills the domain and subsequently solidifies before it is ejected. Inevitably, the process results in and inhomogeneous temperature distribution within the product, causing warpage from residual stresses, resulting in differences between the mold shape and final product. The relationship between the cavity's shape, processing parameters, and the final part geometry is highly nonlinear and surpasses engineering intuition. Thus, PDE-based simulation and numerical design have become an essential tool in process design. While exploring the design space of industrial processes, numerical design optimization requires many function evaluations. Solving the full-field simulation is time-consuming with a large design space; the computational time of design optimization can grow to impractical values. A reduced order model can allow the exploration of a large space at limited accuracy. Like injection molding, the design goals for these processes are diverse and usually product specific. To account for this diversity, as well as for general applicability to all common simulation methods, the focus of this work is on the generation of black-box -- i.e., non-intrusive -- reduced-order models for the full-field solution of partial differential equations. Popular non-intrusive models include proper orthogonal decomposition [1] as a linear model and neural networks as a nonlinear approach. Among the neural network architectures suitable for reduced-order modeling, convolutional neural networks and graph convolutional neural networks have recently received particular attention as predictive models for parameterized PDEs [2, 3]. Using plastic injection molding as a use case, we compare the performance, capabilities, and limitations of generating non-intrusive reduced-order models with POD and graph neural networks. In particular, we focus on their ability to deal with varying geometries and simulation settings, such as mesh types and sizes.