3D Topology Optimization using Convolutional Neural Networks

Banga, Saurabh; Gehani, Harsh; Bhilare, Sanket; Patel, Sagar; Kara, Levent Burak

doi:10.48550/arxiv.1808.07440

Cited by 24 publications

(30 citation statements)

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“…For example, if the element with 0.29 volume density has the prediction error of 0.1, the MAPE for this element can be 34%. This explains one of the reasons that some researchers haven't employed the MAPE for evaluating topology optimization results [11][12][13]. Further, the large MAPE is generated because some outliers around the edge of the optimized beam contribute to most of the errors.…”

Section: Topology Optimization Predictionmentioning

confidence: 99%

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An FEA surrogate model with Boundary Oriented Graph Embedding approach

Fu,

Zhou,

Peddireddy

et al. 2021

Preprint

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In this work, we present a Boundary Oriented Graph Embedding (BOGE) approach for the Graph Neural Network (GNN) to serve as a general surrogate model for regressing physical fields and solving boundary value problems. Providing shortcuts for both boundary elements and local neighbor elements, the BOGE approach can embed structured mesh elements into the graph and performs an efficient regression on large-scale triangular-mesh-based FEA results, which cannot be realized by other machine-learning-based surrogate methods. Focusing on the cantilever beam problem, our BOGE approach cannot only fit the distribution of stress fields but also regresses the topological optimization results, which show its potential of realizing abstract decision-making design process. The BOGE approach with 3-layer DeepGCN model achieves the regression with MSE of 0.011706 (2.41% MAPE) for stress field prediction and 0.002735 MSE (with 1.58% elements having error larger than 0.01) for topological optimization. The overall concept of the BOGE approach paves the way for a general and efficient deep-learning-based FEA simulator that will benefit both industry and design-related areas. KeywordsMachine learning • Graph neural network • Stress field • Solid mechanics • Topology optimization Recently, with the rapid development of Deep Learning (DL) techniques, some researchers employed Convolutional Neural Network (CNN) as the backbone for solving physical field prediction problems, and found out that CNN based surrogate models cannot only solve basic boundary value problems (e.g., solid mechanics [4-6], fluid dynamics [7-9],

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Section: Topology Optimization Predictionmentioning

confidence: 99%

“…etc.) but also perform efficiently on some abstract design problems based on predicted physical field, for instance, topology optimization [10][11][12][13]. However, CNN-based surrogate models still have inevitable disadvantages.…”

Section: Introductionmentioning

confidence: 99%

An FEA surrogate model with Boundary Oriented Graph Embedding approach

Fu,

Zhou,

Peddireddy

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…By doing so, the total number of optimization steps are reduced. Later, Banga et al [23] took a similar idea and extended the work of Sosnovik and Oseledets to 3D design problems and to incorporate additional inputs such as external loads and boundary conditions. More recently, Yu et al [22] proposed a two-stage prediction procedure to produce nearlyoptimal structural design without iterations.…”

Section: Related Workmentioning

confidence: 99%

Speeding up Computational Morphogenesis with Online Neural Synthetic Gradients

Zhang¹,

Chi²,

Chen³

et al. 2021

Preprint

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A wide range of modern science and engineering applications are formulated as optimization problems with a system of partial differential equations (PDEs) as constraints. These PDE-constrained optimization problems are typically solved in a standard discretize-then-optimize approach. In many industry applications that require high-resolution solutions, the discretized constraints can easily have millions or even billions of variables, making it very slow for the standard iterative optimizer to solve the exact gradients. In this work, we propose a general framework to speed up PDE-constrained optimization using online neural synthetic gradients (ONSG) with a novel twoscale optimization scheme. We successfully apply our ONSG framework to computational morphogenesis, a representative and challenging class of PDE-constrained optimization problems. Extensive experiments have demonstrated that our method can significantly speed up computational morphogenesis (also known as topology optimization), and meanwhile maintain the quality of final solution compared to the standard optimizer. On a large-scale 3D optimal design problem with around 1,400,000 design variables, our method achieves up to 7.5x speedup while producing optimized designs with comparable objectives.

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“…This has led the researchers to study how data-driven machine learning algorithms can be used to address this issue. In design optimization, the application of deep learning has been explored in various problems [34], such as topology optimization [35,36,37,38,39], shape parametrization [40,41], meta modeling [42,43,44], material design [45,46,47] and design preference [48].…”

Section: Introductionmentioning

confidence: 99%

Robust Topology Optimization Using Variational Autoencoders

Gladstone¹,

Nabian²,

Keshavarzzadeh³

et al. 2021

Preprint

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Topology Optimization (TO) is the process of finding the optimal arrangement of materials within a design domain by minimizing a cost function, subject to some performance constraints. Robust topology optimization (RTO), as a class of TO problems, also incorporates the effect of input uncertainties, such as uncertainty in loading, boundary conditions, and material properties, and produces a design with the best average performance of the structure while reducing the response sensitivity to input uncertainties. It is computationally expensive to carry out RTO using finite element solvers due to the high dimensional nature of the design space which necessitates multiple iterations and the need to evaluate the probabilistic response using numerous samples. In this work, we use neural network surrogates to enable a faster solution approach via surrogate-based optimization. In particular, we build a Variational Autoencoder (VAE) to transform the the high dimensional design space into a low dimensional one, thus making the design space exploration more efficient. Furthermore, finite element solvers will be replaced by a neural network surrogate that predicts the probabilistic objective function. Also, to further facilitate the design exploration, we limit our search to a subspace, which consists of designs that are solutions to deterministic topology optimization problems under different realizations of input uncertainties. With these neural network approximations, a gradient-based optimization approach is formed to minimize the predicted objective function over the low dimensional design subspace. We demonstrate the effectiveness of the proposed approach on two compliance minimization problems: (1) the design of an L-bracket structure with uncertainty in loading angle, and (2) the design of a heat sink with varying load magnitude in the heat sources. Through these examples, we show that VAE performs well on learning the features of the design from minimal training data. Further, it also shows that converting the design space into a very low dimensional latent space makes the problem computationally efficient, and that the resulting gradient-based optimization algorithm produces optimal designs with lower robust compliances than those observed in the training set.

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3D Topology Optimization using Convolutional Neural Networks

Cited by 24 publications

References 0 publications

An FEA surrogate model with Boundary Oriented Graph Embedding approach

An FEA surrogate model with Boundary Oriented Graph Embedding approach

Speeding up Computational Morphogenesis with Online Neural Synthetic Gradients

Robust Topology Optimization Using Variational Autoencoders

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