Machine learning for topology optimization: physics-based learning through an independent training strategy. (English) Zbl 1507.74329
Summary: The high computational cost of topology optimization has prevented its widespread use as a generative design tool. To reduce this computational cost, we propose an artificial intelligence approach to drastically accelerate topology optimization without sacrificing its accuracy. The resulting AI-driven topology optimization can fully capture the underlying physics of the problem. As a result, the machine learning model, which consists of a convolutional neural network with residual links, is able to generalize what it learned from the training set to solve a wide variety of problems with different geometries, boundary conditions, mesh sizes, volume fractions and filter radius. We train the machine learning model separately from the topology optimization, which allows us to achieve a considerable speedup (up to 30 times faster than traditional topology optimization). Through several design examples, we demonstrate that the proposed AI-driven topology optimization framework is effective, scalable and efficient. The speedup enabled by the framework makes topology optimization a more attractive tool for engineers in search of lighter and stronger structures, with the potential to revolutionize the engineering design process. Although this work focuses on compliance minimization problems, the proposed framework can be generalized to other objective functions, constraints and physics.
MSC:
| 74P15 | Topological methods for optimization problems in solid mechanics |
| 74S99 | Numerical and other methods in solid mechanics |
Keywords:
machine learning; topology optimization; large-scale; 3D convolutional neural network; physics-based machine learning; training setReferences:
| [1] | Chi, H.; Zhang, Y.; Tang, T. L.E.; Mirabella, L.; Dalloro, L.; Song, L.; Paulino, G. H., Universal machine learning for topology optimization, Comput. Methods Appl. Mech. Engrg., 375, Article 112739 pp. (2021) · Zbl 1506.74267 |
| [2] | Christensen, P.; Klarbring, A., An introduction to structural optimization, (Solid Mechanics and Its Applications (2008), Springer Netherlands) · Zbl 1159.90001 |
| [3] | Bendsøe, M.; Sigmund, O., Topology Optimization: Theory, Methods and Applications (2003), Springer Berlin Heidelberg · Zbl 1059.74001 |
| [4] | Sigmund, O., A 99 line topology optimization code written in Matlab, Struct. Multidiscip. Optim., 21, 120-127 (2001) |
| [5] | Andreassen, E.; Clausen, A.; Schevenels, M.; Lazarov, B. S.; Sigmund, O., Efficient topology optimization in Matlab using 88 lines of code, Struct. Multidiscip. Optim., 43, 1, 1-16 (2011) · Zbl 1274.74310 |
| [6] | Talischi, C.; Paulino, G.; Pereira, A.; Menezes, I. M., : A Matlab implementation of a general topology optimization framework using unstructured polygonal finite element meshes, Struct. Multidiscip. Optim., 45, 3, 329-357 (2012) · Zbl 1274.74402 |
| [7] | Borrvall, T.; Petersson, J., Large-scale topology optimization in 3D using parallel computing, Comput. Methods Appl. Mech. Engrg., 190, 46, 6201-6229 (2001) · Zbl 1022.74036 |
| [8] | Schmidt, S.; Schulz, V., A 2589 line topology optimization code written for the graphics card, Comput. Vis. Sci., 14, 6, 249-256 (2011) · Zbl 1380.74100 |
| [9] | Aage, N.; Lazarov, B. S., Parallel framework for topology optimization using the method of moving asymptotes, Struct. Multidiscip. Optim., 47, 4, 493-505 (2013) · Zbl 1274.74302 |
| [10] | Aage, N.; Andreassen, E.; Lazarov, B. S., Topology optimization using PETSc: An easy-to-use, fully parallel, open source topology optimization framework, Struct. Multidiscip. Optim., 51, 3, 565-572 (2015) |
| [11] | Labanda, R., Mathematical programming methods for large-scale topology optimization problems, 240 (2015), (Ph.D. Thesis) |
| [12] | Aage, N.; Andreassen, E.; Lazarov, B. S.; Sigmund, O., Giga-voxel computational morphogenesis for structural design, Nature, 550, 7674, 84-86 (2017) |
| [13] | Wang, S.; Sturler, E.d.; Paulino, G. H., Large-scale topology optimization using preconditioned Krylov subspace methods with recycling, Internat. J. Numer. Methods Engrg., 69, 12, 2441-2468 (2007) · Zbl 1194.74265 |
| [14] | Amir, O.; Aage, N.; Lazarov, B., On multigrid-CG for efficient topology optimization, Struct. Multidiscip. Optim., 48, 815-829 (2014) |
| [15] | Kim, Y. Y.; Yoon, G. H., Multi-resolution multi-scale topology optimization — A new paradigm, Int. J. Solids Struct., 37, 39, 5529-5559 (2000) · Zbl 0981.74044 |
| [16] | Nguyen, T. H.; Paulino, G. H.; Song, J.; Le, C. H., A computational paradigm for multiresolution topology optimization (MTOP), Struct. Multidiscip. Optim., 41, 4, 525-539 (2010) · Zbl 1274.74372 |
| [17] | Liu, H.; Wang, Y.; Zong, H.; Wang, M. Y., Efficient structure topology optimization by using the multiscale finite element method, Struct. Multidiscip. Optim., 58, 4, 1411-1430 (2018) |
| [18] | Senhora, F. V.; Sanders, E. D.; Paulino, G. H., Optimally-tailored spinodal architected materials for multiscale design and manufacturing, Advanced Materials, 2109304 (2022) |
| [19] | K. He, X. Zhang, S. Ren, J. Sun, Deep residual learning for image recognition, in: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2016, pp. 770-778. |
| [20] | Cho, K.; van Merriënboer, B.; Gulcehre, C.; Bahdanau, D.; Bougares, F.; Schwenk, H.; Bengio, Y., Learning phrase representations using RNN encoder-decoder for statistical machine translation, (Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing, EMNLP (2014), Association for Computational Linguistics: Association for Computational Linguistics Doha, Qatar), 1724-1734 |
| [21] | Henrique, B. M.; Sobreiro, V. A.; Kimura, H., Literature review: Machine learning techniques applied to financial market prediction, Expert Syst. Appl., 124, 226-251 (2019) |
| [22] | Mnih, V.; Kavukcuoglu, K.; Silver, D.; Rusu, A. A.; Veness, J.; Bellemare, M. G.; Graves, A.; Riedmiller, M.; Fidjeland, A. K.; Ostrovski, G.; Petersen, S.; Beattie, C.; Sadik, A.; Antonoglou, I.; King, H.; Kumaran, D.; Wierstra, D.; Legg, S.; Hassabis, D., Human-level control through deep reinforcement learning, Nature, 518, 7540, 529-533 (2015) |
| [23] | Bock, F. E.; Aydin, R. C.; Cyron, C. J.; Huber, N.; Kalidindi, S. R.; Klusemann, B., A review of the application of machine learning and data mining approaches in continuum materials mechanics, Front. Mater., 6, 110 (2019) |
| [24] | Ulu, E.; Zhang, R.; Yumer, M. E.; Kara, L. B., A data-driven investigation and estimation of optimal topologies under variable loading configurations, (Zhang, Y. J.; Tavares, J. M.R. S., Computational Modeling of Objects Presented in Images. Fundamentals, Methods, and Applications (2014), Springer International Publishing: Springer International Publishing Cham), 387-399 |
| [25] | Sosnovik, I.; Oseledets, I. V., Neural networks for topology optimization (2017), arXiv:1709.09578 |
| [26] | Banga, S.; Gehani, H.; Bhilare, S.; Patel, S.; Kara, L., 3D Topology optimization using convolutional neural networks (2018), ArXiv arXiv:1808.07440 |
| [27] | Kallioras, N. A.; Kazakis, G.; Lagaros, N. D., Accelerated topology optimization by means of deep learning, Struct. Multidiscip. Optim., 62, 3, 1185-1212 (2020) |
| [28] | Keshavarzzadeh, V.; Alirezaei, M.; Tasdizen, T.; Kirby, R. M., Image-based multiresolution topology optimization using deep disjunctive normal shape model, Comput. Aided Des., 130, Article 102947 pp. (2021) |
| [29] | Yu, Y.; Hur, T.; Jung, J.; Jang, I. G., Deep learning for determining a near-optimal topological design without any iteration, Struct. Multidiscip. Optim., 59, 3, 787-799 (2019) |
| [30] | Nie, Z.; Lin, T.; Jiang, H.; Kara, L. B., Topologygan: Topology optimization using generative adversarial networks based on physical fields over the initial domain, J. Mech. Des., 143, 3, Article 031715 pp. (2021) |
| [31] | Li, B.; Huang, C.; Li, X.; Zheng, S.; Hong, J., Non-iterative structural topology optimization using deep learning, Comput. Aided Des., 115, 172-180 (2019) |
| [32] | Zhang, Y.; Chen, A.; Peng, B.; Zhou, X.; Wang, D., A deep convolutional neural network for topology optimization with strong generalization ability (2019), arXiv:1901.07761 |
| [33] | Rawat, S.; Shen, M. H., Application of adversarial networks for 3D structural topology optimization, (WCX SAE World Congress Experience (2019), SAE International) |
| [34] | Abueidda, D. W.; Koric, S.; Sobh, N. A., Topology optimization of 2D structures with nonlinearities using deep learning, Comput. Struct., 237, Article 106283 pp. (2020) |
| [35] | Bendsøe, M., Optimal shape design as a material distribution problem, Struct. Optim., 1, 193-202 (1989) |
| [36] | Bendsøe, M.; Sigmund, O., Material interpolation schemes in topology optimization, Arch. Appl. Mech., 69, 9-10, 635-654 (1999) · Zbl 0957.74037 |
| [37] | Wang, F.; Lazarov, B.; Sigmund, O., On projection methods, convergence and robust formulations in topology optimization, Struct. Multidiscip. Optim., 43, 6, 767-784 (2011) · Zbl 1274.74409 |
| [38] | Bourdin, B., Filters in topology optimization, Internat. J. Numer. Methods Engrg., 50, 9, 2143-2158 (2001) · Zbl 0971.74062 |
| [39] | Zegard, T.; Paulino, G., Bridging topology optimization and additive manufacturing, Struct. Multidiscip. Optim., 53, 1, 175-192 (2016) |
| [40] | Talischi, C.; Paulino, G., An operator splitting algorithm for Tikhonov-regularized topology optimization, Comput. Methods Appl. Mech. Engrg., 253, 599-608 (2013) · Zbl 1297.74090 |
| [41] | LeCun, Y.; Bengio, Y.; Hinton, G., Deep learning, Nature, 521, 7553, 436-444 (2015) |
| [42] | A. Krizhevsky, I. Sutskever, G.E. Hinton, Imagenet classification with deep convolutional neural networks, in: Advances in Neural Information Processing Systems, 2012, pp. 1097-1105. |
| [43] | Lathuilière, S.; Mesejo, P.; Alameda-Pineda, X.; Horaud, R., A comprehensive analysis of deep regression (2018), ArXiv |
| [44] | Ioffe, S.; Szegedy, C., Batch normalization: Accelerating deep network training by reducing internal covariate shift (2015), ArXiv arXiv:1502.03167 |
| [45] | Mises, R.v., On Saint Venant’s principle, Bull. Amer. Math. Soc., 51, 8, 555-562 (1945) · Zbl 0063.04019 |
| [46] | Timoshenko, S., History of Strength of Materials: With a Brief Account of the History of Theory of Elasticity and Theory of Structures (1983), Courier Corporation |
| [47] | K. He, X. Zhang, S. Ren, J. Sun, Delving deep into rectifiers: Surpassing human-level performance on imagenet classification, in: Proceedings of the IEEE International Conference on Computer Vision, 2015, pp. 1026-1034. |
| [48] | Paszke, A.; Gross, S.; Massa, F.; Lerer, A.; Bradbury, J.; Chanan, G.; Killeen, T.; Lin, Z.; Gimelshein, N.; Antiga, L.; Desmaison, A.; Kopf, A.; Yang, E.; DeVito, Z.; Raison, M.; Tejani, A.; Chilamkurthy, S.; Steiner, B.; Fang, L.; Bai, J.; Chintala, S., PyTorch: An imperative style, high-performance deep learning library, (Advances in Neural Information Processing Systems, vol. 32 (2019), Curran Associates, Inc.), 8024-8035 |
| [49] | Kingma, D. P.; Ba, J., Adam: A method for stochastic optimization (2014), arXiv preprint arXiv:1412.6980 |
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