eCNNTO: A Highly Generalizable ConvNet for Accelerating Topology Optimization

2026-06-18

AI Summary

This work addresses the high computational cost of traditional topology optimization, which relies on repeated finite element analyses on fine-resolution meshes, and the limited structural continuity in existing data-driven approaches that often neglect spatial correlations among elements. To overcome these challenges, the authors propose eCNNTO, a method that explicitly models the spatial dependencies between each element and its neighborhood using a convolutional neural network with residual connections. Innovatively, the training dataset is constructed from density histories collected during the later stages of optimization, substantially enhancing data efficiency and generalization. The approach supports two- and three-dimensional problems under multiple loading conditions, diverse geometries, and varying mesh resolutions. In various test cases, eCNNTO achieves 90%–97% reduction in iteration count with only a small amount of training data and effectively handles significant variations in boundary conditions, loads, and non-design regions.

Abstract

This work proposes an element-based Convolutional Neural Network (CNN) to accelerate density-based Topology Optimization (TO), termed eCNNTO. TO generally undergoes a large number of iterations, where finite element analysis is performed in every iteration, leading to the efficiency bottleneck especially when dense meshes are used to achieve high-resolution designs. To address this limitation, eCNNTO is proposed to build upon Kallioras et al. (2020), where a Deep Belief Network (DBN) was trained for every element to predict its near-optimal density from its early history, thereby skipping the great majority of iterations and significantly accelerating the TO procedure. However, the method lacks spatial correlations among neighboring elements and may lead to disconnected features in the final structure. The proposed method employs CNN with residual connections to address this issue. On top of it, a novel training strategy is introduced to further enhance the optimization efficiency, where the training dataset consists of the final stage density histories rather than early ones. This change can also help reduce the required training data size. eCNNTO requires only a small dataset to train and yet it can be generalized to problems with largely different boundary conditions, loading cases, design domain geometries, mesh resolutions, as well as non-design domains. In the end, the generalization capabilities and efficiency of eCNNTO are demonstrated through a variety of examples in two and three dimensions, achieving up to 90% and 97% reduction of iterations, respectively.

Problem

• Topology Optimization
• Computational Efficiency
• Spatial Correlation
• High-Resolution Mesh
• Finite Element Analysis

Innovation

• Convolutional Neural Network
• Topology Optimization
• Residual Connections
• Generalization
• Training Strategy