Non-iterative structural topology optimization using deep learning

Li, Baotong; Huang, Congjia; Li, Xin; Zheng, Shuai; Hong, Jun

doi:10.1016/j.cad.2019.05.038

Cited by 77 publications

(24 citation statements)

References 28 publications

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“…This method has good versatility at a given mesh resolution but requires retraining the neural network for other structures with a different resolution. Li et al [58] implemented topology optimization without iteration by using a generative adversarial network (GAN) and used another GAN as a post-processing method to improve the resolution of the final configuration.…”

Section: Introductionmentioning

confidence: 99%

Efficient, high-resolution topology optimization method based on convolutional neural networks

Liu

Wen

et al. 2021

Front. Mech. Eng.

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Topology optimization is a pioneer design method that can provide various candidates with high mechanical properties. However, high resolution is desired for optimum structures, but it normally leads to a computationally intractable puzzle, especially for the solid isotropic material with penalization (SIMP) method. In this study, an efficient, high-resolution topology optimization method is developed based on the superresolution convolutional neural network (SRCNN) technique in the framework of SIMP. SRCNN involves four processes, namely, refinement, path extraction and representation, nonlinear mapping, and image reconstruction. High computational efficiency is achieved with a pooling strategy that can balance the number of finite element analyses and the output mesh in the optimization process. A combined treatment method that uses 2D SRCNN is built as another speed-up strategy to reduce the high computational cost and memory requirements for 3D topology optimization problems. Typical examples show that the high-resolution topology optimization method using SRCNN demonstrates excellent applicability and high efficiency when used for 2D and 3D problems with arbitrary boundary conditions, any design domain shape, and varied load.

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Section: Introductionmentioning

confidence: 99%

Efficient, high-resolution topology optimization method based on convolutional neural networks

Liu

Wen

et al. 2021

Front. Mech. Eng.

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“…They concatenate their design variables with the noise vector and feed them to their CWGAN to generate the cantilever beam that corresponds to the design variables. A two-stage hierarchical prediction-refinement GAN-based framework [15] is used to predict the low resolution near-optimal structure and its corresponding refined structure in high resolution. Their training data set contains 9,900 pairs of low-resolution (40 x 40) and high-resolution (160 x 160) data, and the method achieves a 9.1 % MSE for high resolution predictions.…”

Section: Introductionmentioning

confidence: 99%

GANTL: Towards Practical and Real-Time Topology Optimization with Conditional GANs and Transfer Learning

Behzadi¹,

Ilieş²

2021

Preprint

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Many machine learning methods have been recently developed to circumvent the high computational cost of the gradient-based topology optimization. These methods typically require extensive and costly datasets for training, have a difficult time generalizing to unseen boundary and loading conditions and to new domains, and do not take into consideration topological constraints of the predictions, which produces predictions with inconsistent topologies.We present a deep learning method based on generative adversarial networks for generative design exploration. The proposed method combines the generative power of conditional GANs with the knowledge transfer capabilities of transfer learning methods to predict optimal topologies for unseen boundary conditions. We also show that the knowledge transfer capabilities embedded in the design of the proposed algorithm significantly reduces the size of the training dataset compared to the traditional deep learning neural or adversarial networks. Moreover, we formulate a topological loss function based on the bottleneck distance obtained from the persistent diagram of the structures and demonstrate a significant improvement in the topological connectivity of the predicted structures. We use numerous examples to explore the efficiency and accuracy of the proposed approach for both seen and unseen boundary conditions in 2D.

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“…Led by this promise, recent years have seen a surge in publications on the application of deep learning [23] to topology optimization within a variety of problems such as minimum compliance [20,45,10,42,11,29,21], thermal compliance [27,25,26], micro-structure design [2,37,41,22,12] and generative design [32]. Despite these efforts, deep learning has yet to make a major impact within topology optimization, and only performs at a similar level to traditional topology optimization methods at very low design resolutions, or for highly restricted problem domains and boundary conditions, where the cost of generating a synthetic dataset and training a neural network is not prohibitive.…”

Section: Introductionmentioning

confidence: 99%

De-homogenization using Convolutional Neural Networks

Elingaard,

Aage,

Bærentzen

et al. 2021

Preprint

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This paper presents a deep learning-based de-homogenization method for structural compliance minimization. By using a convolutional neural network to parameterize the mapping from a set of lamination parameters on a coarse mesh to a one-scale design on a fine mesh, we avoid solving the least square problems associated with traditional de-homogenization approaches and save time correspondingly. To train the neural network, a two-step custom loss function has been developed which ensures a periodic output field that follows the local lamination orientations. A key feature of the proposed method is that the training is carried out without any use of or reference to the underlying structural optimization problem, which renders the proposed method robust and insensitive wrt. domain size, boundary conditions, and loading. A post-processing procedure utilizing a distance transform on the output field skeleton is used to project the desired lamination widths onto the output field while ensuring a predefined minimum length-scale and volume fraction. To demonstrate that the deep learning approach has excellent generalization properties, numerical examples are shown for several different load and boundary conditions. For an appropriate choice of parameters, the de-homogenized designs perform within 7 − 25% of the homogenization-based solution at a fraction of the computational cost. With several options for further improvements, the scheme may provide the basis for future interactive high-resolution topology optimization. Figure 1: De-homogenization of a 200 × 50 homogenization-based solution onto a fine mesh of 8000×2000 elements. Compliance of the de-homogenized design is within 17% of the homogenization solution, adheres to a predefined minimum relative thickness, and has been de-homogenized in just 15 seconds on a modern day laptop.

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Non-iterative structural topology optimization using deep learning

Cited by 77 publications

References 28 publications

Efficient, high-resolution topology optimization method based on convolutional neural networks

Efficient, high-resolution topology optimization method based on convolutional neural networks

GANTL: Towards Practical and Real-Time Topology Optimization with Conditional GANs and Transfer Learning

De-homogenization using Convolutional Neural Networks

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