基于扩散模型的拓扑优化研究
Topology Optimization Based on Diffusion Model
DOI: 10.12677/JSTA.2024.121003, PDF,    科研立项经费支持
作者: 崔富豪, 韩佳辰, 张 楠, 马朝青*：烟台大学计算机与控制工程学院，山东 烟台；姜 滔：烟台大学科技处，山东 烟台
关键词: DDIM；拓扑优化；U-NET；DeepLearning；SE-ResNet； DDIM； Topology Optimization； U-Net； Deep Learning； SE-ResNet
摘要: 拓扑优化是工业设计领域中常见的数学方法，旨在给定的物理领域内，满足各种约束条件、负载和其他边界条件等前提下，生成最佳的拓扑结构。传统的拓扑优化大多都依赖有限元方法(FEM)，然而有限元方法的迭代计算很大程度上增加了拓扑优化的时间成本和算力成本。如今，机器学习和深度学习在图像生成领域内的快速发展为拓扑优化的发展带来了机遇。扩散模型是一种无监督图像生成模型，因生成效果优秀、细节完美等特点等得到广泛使用。本文将在扩散模型的基础上提出新的网络结构，让其适应拓扑优化生成特性，根据特定信息生成与之对应的最优拓扑优化结果。
Abstract: Topology optimization is a common mathematical method in the field of industrial design, aiming to generate the best topology structure in a physical field under various constraints, loads, and boundary conditions. Most of the traditional topology optimization methods are based on finite element method (FEM) the iterative calculation of which increases the time cost and the demand of computing power greatly. Nowadays, the rapid developments of machine learning and deep learning in the field of image generation have brought opportunities to improve topology optimization methods. Diffusion model is a kind of unsupervised image generation model. Since the model can generate images with more detail efficiently, it is widely used in different fields. In this paper, a novel model is proposed based on the diffusion model for topology optimization. Given the characteristic of topology optimization, this model can generate optimal topology structures according to their specific information.
文章引用：崔富豪, 姜滔, 韩佳辰, 张楠, 马朝青. 基于扩散模型的拓扑优化研究[J]. 传感器技术与应用, 2024, 12(1): 16-26. https://doi.org/10.12677/JSTA.2024.121003

参考文献

[1] Sigmund, O. (2001) A 99 Line Topology Optimization Code Written in Matlab. Structural and Multidisciplinary Optimiza-tion, 21, 120-127. [Google Scholar] [CrossRef] 
[2] Xu, S., Liu, J., Zou, B., Li, Q.H. and Ma, Y.S. (2021) Stress Constrained Multi-Material Topology Optimization with the Ordered SIMP Method. Computer Methods in Applied Mechanics and Engineering, 373, Article ID: 113453. [Google Scholar] [CrossRef] 
[3] Zhang, S., Li, H. and Huang, Y. (2021) An Improved Mul-ti-Objective Topology Optimization Model Based on SIMP Method for Continuum Structures Including Self-Weight. Structural and Multidisciplinary Optimization, 63, 211-230. [Google Scholar] [CrossRef] 
[4] Yu, H., He, F. and Pan, Y. (2020) A Scalable Region-Based Level Set Method Using Adaptive Bilateral Filter for Noisy Image Segmentation. Multimedia Tools and Applications, 79, 5743-5765. [Google Scholar] [CrossRef] 
[5] Wang, M.Y., Wang, X. and Guo, D. (2003) A Level Set Method for Structural Topology Optimization. Computer Methods in Applied Mechanics and Engineering, 192, 227-246. [Google Scholar] [CrossRef] 
[6] Xia, Q., Shi, T. and Xia, L. (2018) Topology Optimization for Heat Conduction by Combining Level Set Method and BESO Method. International Journal of Heat and Mass Transfer, 127, 200-209. [Google Scholar] [CrossRef] 
[7] Bendsøe, M.P. and Kikuchi, N. (1988) Generating Optimal Topologies in Structural Design Using a Homogenization Method. Computer Methods in Applied Mechanics and Engineering, 71, 197-224. [Google Scholar] [CrossRef] 
[8] Allaire, G., Geoffroy-Donders, P. and Pantz, O. (2019) To-pology Optimization of Modulated and Oriented Periodic Microstructures by the Homogenization Method. Computers & Mathematics with Applications, 78, 2197-2229. [Google Scholar] [CrossRef] 
[9] Gao, J., Li, H., Gao, L. and Xiao, M. (2018) Topological Shape Optimization of 3D Micro-Structured Materials Using Energy-Based Homogenization Method. Advances in Engineering Software, 116, 89-102. [Google Scholar] [CrossRef] 
[10] Xie, Y.M. and Steven, G.P. (1997) Basic Evolutionary Structural Optimization. In: Xie, Y.M. and Steven, G.P., Eds., Evolutionary Structural Optimization, Springer, London, 12-29. [Google Scholar] [CrossRef] 
[11] Xia, L., Xia, Q., Huang, X. and Xie, Y.M. (2018) Bi-Directional Evolutionary Structural Optimization on Advanced Structures and Materials: A Comprehensive Review. Archives of Computational Methods in Engineering, 25, 437-478. [Google Scholar] [CrossRef] 
[12] Bisbo, M.K. and Hammer, B. (2020) Efficient Global Structure Optimization with a Machine-Learned Surrogate Model. Physical Review Letters, 124, Article ID: 086102. [Google Scholar] [CrossRef] 
[13] Goodfellow, I., Pouget-Abadie, J., Mirza, M., et al. (2014) Generative Adversarial Nets. Proceedings of the 27th International Conference on Neural Information Processing Sys-tems, Montreal, 8-13 December 2014, 2672-2680.
[14] Creswell, A., White, T., Dumoulin, V., et al. (2018) Generative Adversarial Networks: An Overview. IEEE Signal Processing Magazine, 35, 53-65. [Google Scholar] [CrossRef] 
[15] Wang, K., Gou, C., Duan, Y., et al. (2017) Generative Adversari-al Networks: Introduction and Outlook. IEEE/CAA Journal of Automatica Sinica, 4, 588-598. [Google Scholar] [CrossRef] 
[16] Rawat, S. and Shen, M.H.H. (2019) A Novel Topology Optimiza-tion Approach Using Conditional Deep Learning. arXiv: 1901.04859.
[17] Sosnovik, I. and Oseledets, I. (2019) Neural Networks for Topology Optimization. Russian Journal of Numerical Analysis and Mathematical Modelling, 34, 215-223. [Google Scholar] [CrossRef] 
[18] Gauthier, J. (2014) Conditional Generative Adversarial Nets for Convolutional Face Generation. Class Project for Stanford CS231N: Convolutional Neural Networks for Visual Recogni-tion, 2014, 2.
[19] Behzadi, M.M. and Ilieş, H.T. (2022) GANTL: Toward Practical and Real-Time Topology Optimi-zation with Conditional Generative Adversarial Networks and Transfer Learning. Journal of Mechanical Design, 144, Article ID: 021711. [Google Scholar] [CrossRef] 
[20] Yu, Y., Hur, T., Jung, J. and Jang, I.G. (2019) Deep Learning for Determining a Near-Optimal Topological Design without Any Iteration. Structural and Multidisciplinary Optimization, 59, 787-799. [Google Scholar] [CrossRef] 
[21] Bendsøe, M.P. (1989) Optimal Shape Design as a Material Dis-tribution Problem. Structural Optimization, 1, 193-202. [Google Scholar] [CrossRef] 
[22] Ho, J., Jain, A. and Abbeel, P. (2020) Denoising Diffusion Probabilistic Models. Advances in Neural Information Processing Systems, 33, 6840-6851.
[23] Song, J., Meng, C. and Ermon, S. (2020) Denoising Diffusion Implicit Models. arXiv: 2010.02502.
[24] Nie, Z., Lin, T., Jiang, H. and Kara, L.B. (2021) Topologygan: Topology Optimization Using Generative Adversarial Networks Based on Physical Fields over the Initial Domain. Journal of Mechanical Design, 143, Article ID: 031715. [Google Scholar] [CrossRef] 

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