Deep learning for determining a near-optimal topological design without any iteration (1801.05463v3)

Abstract: In this study, we propose a novel deep learning-based method to predict an optimized structure for a given boundary condition and optimization setting without using any iterative scheme. For this purpose, first, using open-source topology optimization code, datasets of the optimized structures paired with the corresponding information on boundary conditions and optimization settings are generated at low (32 x 32) and high (128 x 128) resolutions. To construct the artificial neural network for the proposed method, a convolutional neural network (CNN)-based encoder and decoder network is trained using the training dataset generated at low resolution. Then, as a two-stage refinement, the conditional generative adversarial network (cGAN) is trained with the optimized structures paired at both low and high resolutions, and is connected to the trained CNN-based encoder and decoder network. The performance evaluation results of the integrated network demonstrate that the proposed method can determine a near-optimal structure in terms of pixel values and compliance with negligible computational time.

Deep Learning for Non-Iterative Topological Design Optimization

This paper presents a novel approach that leverages deep learning techniques to determine near-optimal topological designs devoid of iterative processes. Traditional topology optimization often requires extensive computational resources, primarily due to iteration-heavy processes involving numerous design variables. This paper circumvents these challenges by introducing a deep learning methodology that streamlines the optimization procedure while maintaining the efficacy of the resultant designs.

Methodology

The approach utilizes a combination of deep learning architectures including convolutional neural networks (CNNs) and generative adversarial networks (GANs). Initially, a CNN-based encoder-decoder network is trained using low-resolution data. This dataset is prepared through open-source topology optimization tools, providing structures paired with optimization parameters and boundary conditions. The innovation lies in eschewing traditional iterative schemes, instead directly predicting material distributions for topological designs.

Following this, a two-stage refinement leverages conditional GANs (cGANs) to enhance the structural resolution prediction from low to high resolutions. The cGAN operates on datasets that relate low-resolution optimized structures to their high-resolution counterparts, effectively bridging the fidelity gap induced by resolution limitations.

Numerical Results and Implications

The numerical evaluations of this integrated network reveal its capability to generate near-optimal structures efficiently, with minimal computational overhead. Specifically, the proposed method achieves this with computational times that are merely 0.06% of conventional topology optimization processes when evaluated at a high resolution (128x128). Moreover, pixel-wise errors in produced high-resolution structures remain below 2.72%, demonstrating precise conformance to optimization goals.

Despite promising results, the methodology is found to struggle in scenarios involving structural discontinuities. This challenge points to the need for augmenting the model to consider measures of structural integrity such as compliance directly.

Practical and Theoretical Implications

From a practical standpoint, this method significantly reduces the computational burden traditionally associated with topological optimization, potentially enabling real-time applications in complex scenarios. Theoretically, integrating deep learning into the paradigm of engineering design optimization opens new research avenues, particularly in the handling of complex boundary conditions and model scalability.

Future Directions

The authors acknowledge several limitations, including the constraint of fixed regular mesh structures and the need for a more expansive dataset to incorporate intricate boundary conditions and optimization settings. Future developments may involve extending the method to accommodate non-Euclidean meshes and larger design models, while also integrating measures for maintaining structural continuity to address compliance discrepancies.

Overall, this work highlights a significant step toward embedding deep learning frameworks in topology optimization, offering a compelling avenue for both enhancing design processes and furthering academic research in computational optimization methodologies.