Generating three-dimensional structural topologies via a U-Net convolutional neural network

Zheng, Shuai; He, Zhenzhen; Liu, Honglei

doi:10.1016/j.tws.2020.107263

Cited by 27 publications

(11 citation statements)

References 28 publications

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“…11 Shuai et al extended their work to 3D problems. 12 Abueidda. et al combined the U-Net with Resnet on solving topology optimization.…”

Section: Literature Reviewmentioning

confidence: 99%

“…The first approach substitutes the iterative process with a non-iterative neural network. [9][10][11][12][13][14][15][16] The primary advantage of this approach is its ability to bypass the iterative procedure, enabling rapid generation of optimal topologies in mere seconds. However, this method presents challenges, including limited generalization capabilities-particularly in scenarios with unseen boundary conditions-and the potential generation of disconnect structures.…”

Section: Introductionmentioning

confidence: 99%

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TO‐NODE: Topology optimization with neural ordinary differential equation

Ma,

De Meter,

Basu

2024

Numerical Meth Engineering

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Deep learning methods have become attractive recently to accelerate topology optimization (TO) because of their capability to save huge computational costs with negligible sacrifice in the quality of final topologies. However, most current approaches rely on numerical mechanics platforms for training which incur significant computation costs. Further, current approaches are not suited for dynamically changing boundary conditions. This is because these deep learning frameworks once trained using results generated with a specific set of boundary conditions do not readily adapt to others. In this article, we present a novel approach to leverage the abilities of deep learning models for TO. We demonstrate that optimization can be achieved using a neural ordinary differential equation. The evolution of the design variable in each iteration of TO is then achieved by numerical integration of this neural differential equation with respect to the starting design. To improve the quality of the results, two levels of generative adversarial networks are also introduced, at the sequence, and image levels, respectively. The proposed machine learning framework is capable of generating full optimization paths relevant to TO in high resolution within seconds and can address novel unseen boundary conditions.

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“…11 Shuai et al extended their work to 3D problems. 12 Abueidda. et al combined the U-Net with Resnet on solving topology optimization.…”

Section: Literature Reviewmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

TO‐NODE: Topology optimization with neural ordinary differential equation

Ma,

De Meter,

Basu

2024

Numerical Meth Engineering

View full text Add to dashboard Cite

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“…However, some invalid designs are reported in the paper, making the method only suitable for preliminary design 15 . Zheng et al extended the work into the 3D design space 16 . One great advantage of the method is that they can vary the initial design domain sizes by the adaptive sizing technique, which significantly expands the application of deep learning in topology optimization design.…”

Section: Introductionmentioning

confidence: 99%

“…15 Zheng et al extended the work into the 3D design space. 16 One great advantage of the method is that they can vary the initial design domain sizes by the adaptive sizing technique, which significantly expands the application of deep learning in topology optimization design. Once again, the limitation of the network is that it cannot be applied to solve every topology optimization problem without prior training.…”

Section: Introductionmentioning

confidence: 99%

Learning topology optimization process via convolutional long‐short‐term memory autoencoder‐decoder

DeMeter

Basu

2023

Numerical Meth Engineering

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This article proposed an autoencoder-decoder architecture with convolutional long-short-term memory (ConvLSTM) cell for the purpose of learning topology optimization iterations. The overall topology optimization process is treated as time-series data, with each iteration as a single step. The first few steps are fed into the encoder to generate encoder embedding, which is fed into the decoder. The decoder uses the encoder embedding as input and generates the result at each future step until the end of iteration. To train the proposed neural network, a large dataset is generated by a conventional topology optimization method, that is, solid isotropic material with penalization for intermediate densities, with randomly picked boundary conditions, load conditions, and volume constraints. Unlike other deep learning models introduced before, the proposed method can learn each topology optimization step iteratively and present the full optimization path. Furthermore, the proposed method can be extended to give solutions to unseen boundary and load conditions with a significant reduction in computation cost in a little sacrifice on the performance of the optimum design.

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“…Many researchers have developed data-driven models to capture physical responses [4,5,6,7,8,9]. Additionally, data-driven models have been developed to obtain near-optimal topologies for metamaterials and structures, where 2D and 3D domains, linear and nonlinear constraints, and material and geometric nonlinearities have been considered [10,11,12,13,14]. However, usually one needs a large number of data points to accurately capture intricate relationships between the input and output, making the data generation the bottleneck step in most cases.…”

Section: Introductionmentioning

confidence: 99%

A deep learning energy method for hyperelasticity and viscoelasticity

Abueidda,

Koric,

Al-Rub

et al. 2022

Preprint

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The potential energy formulation and deep learning are merged to solve partial differential equations governing the deformation in hyperelastic and viscoelastic materials. The presented deep energy method (DEM) is self-contained and meshfree. It can accurately capture the three-dimensional (3D) mechanical response without requiring any time-consuming training data generation by classical numerical methods such as the finite element method. Once the model is appropriately trained, the response can be attained almost instantly at any point in the physical domain, given its spatial coordinates. Therefore, the deep energy method is potentially a promising standalone method for solving partial differential equations describing the mechanical deformation of materials or structural systems and other physical phenomena.

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Generating three-dimensional structural topologies via a U-Net convolutional neural network

Cited by 27 publications

References 28 publications

TO‐NODE: Topology optimization with neural ordinary differential equation

TO‐NODE: Topology optimization with neural ordinary differential equation

Learning topology optimization process via convolutional long‐short‐term memory autoencoder‐decoder

A deep learning energy method for hyperelasticity and viscoelasticity

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