Topology Optimization with Learned Displacement Fields: An Analysis of Model-Driven Errors

Topology optimization enables the creation of highly efficient structures by optimally distributing material within a design domain. However, traditional methods rely on repeated Finite Element Method (FEM) analyses, leading to high computational costs, particularly for large-scale or complex problems. To mitigate this, recent research has focused on integrating machine learning methodologies to replace costly steps with faster predictions using metamodels. This study presents a metamodel for predicting displacement fields in a 2D cantilever beam topology optimization problem. A U-Net model architecture, originally developed for image segmentation, presented an excellent trade-off between accuracy and training time, measured using the Mean Squared Error (MSE). The dataset was generated using a parameterized Solid Isotropic Material with Penalization (SIMP) method, requiring 35 hours of computation and approximately 20 hours of offline metamodel training. For a domain of size 180 by 60, the metamodel achieved a 6.5 times speedup over traditional methods. The predicted displacement fields closely resembled the ground truth values, presenting a relatively low error. However, pixel-wise differences led to notable deviations in final optimized topologies. Sensitivity analysis showed that, due to localized high displacement gradients, the metamodel often overestimated the importance of the wrong locations, namely, the load application location. Despite these challenges, the metamodel showed strong potential to accelerate topology optimization. It may also significantly reduce computation time in standalone FEM simulations across various engineering applications, since the metamodel achieved reasonable accuracy in its predictions.