Dynamic graph-based convergence acceleration for topology optimization in unstructured meshes

Topology optimization need acceleration to reduce computational costs. While various efforts have employed Convolutional Neural Networks (CNNs) for this purpose, they aren't suitable for unstructured meshes. This study introduces a novel methodology for accelerating topology optimization under unstructured meshes using a dynamic graph-based neural network. It transforms information about the connectivity between elements and vertices of the finite element mesh into graph data, which includes node and edge features. By combining the dynamic graph concept and edge convolution, our model is designed to learn and adapt to information distributed across unstructured spaces. The predicted near-optimal topologies from our model serve as the initial designs for topology optimization to expedite convergence. To assess the effectiveness of the dynamic graph approach and edge convolution, we construct and compare two types of graph neural networks. Specifically, we achieve a 33% acceleration in topology optimization convergence with our proposed model. To evaluate the broad applicability of our method, we apply the trained model to numerical examples with domain shapes, the number of elements, and the number of loads differing from those in the training data. As a result, the proposed method predicts layouts without requiring any modifications. This study provides a generally applicable approach to expedite topology optimization for unstructured meshes, leveraging training data encompassing a wide spectrum of design conditions. Our research not only offers a means to accelerate topology optimization but also demonstrates its potential applicability to a wide array of practical design problems, including those involving unstructured meshes.