This case study employs surrogate models to replace expensive computer simulations, a common practice for conventional Finite Element Analysis (FEA) solvers. Model discretization and meshing are critical and time-consuming steps in FEA. In parametric studies requiring numerous iterations to create model meshes, morphing is a useful technique for adjusting design parameters and can be combined with automatic mesh generation tools. This approach ensures model robustness and better convergence.

To enhance predictive capabilities, a Graph Neural Network (GNN)–based surrogate model was implemented using a Python library. Node features, including coordinates and boundary conditions, were provided, and edge indices were computed. These inputs were utilized by the GNN, with nodal stresses and displacements from the FEA serving as target variables in a supervised learning context. A comprehensive dataset, encompassing a wide range of configurations, was generated to capture all possible variations. The results demonstrated a strong correlation between the displacements and stresses obtained from the FEA and the corresponding predictions from the GNN model for both test and validation data.

In related research, authors have developed surrogate model-assisted optimization algorithms for single and multi-objective optimization. One of these algorithms was utilized in this case study on an actual engineering problem to generate the Pareto front. The results showed considerable improvement in Normalized Hyper Volume values compared to reference surrogate-assisted multi-objective optimization problems, with an improved and more evenly spaced Pareto front.