Deep learning for determining a near-optimal topological design without any iteration

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  32) and high (128  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 nearoptimal structure in terms of pixel values and compliance with negligible computational time.

TopologyGAN: Topology Optimization Using Generative Adversarial Networks Based on Physical Fields Over the Initial Domain

“…To realize an end-to-end topology optimization from prescribed boundary conditions, Yu et al [35] propose a CNN-based encoder-decoder for the generation of low-resolution structures, which are then passed through a super-resolution GAN to generate the final results. Sharpe and Seepersad [37] explore the use of cGANs as a means of generating a compact latent representation of structures resulting from topology optimization.…”

“…In recent years, new data-driven methods for topology optimization have been proposed to accelerate the process. Deep learning methods have shown promise in efficiently producing near-optimal results with respect to shape similarity as well as compliance with negligible run-time cost [34][35][36][37][38][39][40][41]. Theory-guided machine learning methods use domain-specific theories to establish the mapping between the design variables and the external boundary conditions [42][43][44].…”

Deep Generative Design: Integration of Topology Optimization and Generative Models

“…In gradient-based optimization, the sensitivity analysis of objective and constraint function with respect to each design variable is required to provide accurate search direction to the optimizer. Therefore, the sensitivity analysis with respect to the density of elements can be given by (4) under the assumption that all elements have a unit volume. On the other hand, the optimality criteria (OC) method, one of the classical approaches to structural optimization problems, is employed in this paper.…”

Topologieoptimierung mittels Deep Learning ohne voroptimierte Trainingsdaten

“…Beispielsweise sind KNN in der Lage, die auf Bildern dargestellten Objekte anhand ihrer Form und Farbe zu erkennen oder Weltmeister im Brettspiel "Go" [5], [6] Es gibt bereits einige Versuche in diesem Bereich. So verwenden [9][10][11] viele tausende topologieoptimierte Geometrien als Trainingsdatensätze für die KNN. In [12] wurde ein anderer Ansatz entwickelt, bei dem Zwischenergebnisse konventioneller TO (das Ergebnis einer begrenzten Anzahl von Optimierungsiterationen konventioneller TO -inklusive der darin ermittelten Gradienten) als Trainingsdatensätze für den KNN verwendet werden.…”