Graph neural networks and implicit neural representation for near-optimal topology prediction over irregular design domains

This paper proposes a deep neural network-based topology optimization acceleration method for irregular design domains that predicts (near-)optimal topologies. A topology optimization problem is a complex non-Euclidean data, which can be embedded in a graph form, and a graph neural network encodes it to Euclidean data such as vectors and matrices. The encoded information is applied to a multi-layer perceptron-based implicit neural representation model, and the multi-layer perceptron approximator predicts the compliance optimal material distribution. The prediction performance of the proposed encoder-approximator architecture is evaluated for several topology optimization problems. The trained network provides 96.6% compliance accuracy, except for 8.0% of the outliers. The two criteria have been investigated to estimate potential outliers, and post-optimization can resolve the outlier within fewer iterations than the original optimization.