Abstract
We present and publish the DL4TO software library – a Python library for three-dimensional topology optimization. The framework is based on PyTorch and allows easy integration with neural networks. The library fills a critical void in the current research toolkit on the intersection of deep learning and topology optimization. We present the structure of the library’s main components and how it enabled the incorporation of physics concepts into deep learning models.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The DL4TO library is publicly available at https://github.com/dl4to/dl4to.
References
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)
Abueidda, D.W., Koric, S., Sobh, N.A.: Topology optimization of 2d structures with nonlinearities using deep learning. Comput. Structures 237, 106283 (2020)
Banga, S., Gehani, H., Bhilare, S., Patel, S., Kara, L.: 3d topology optimization using convolutional neural networks. arXiv preprint arXiv:1808.07440 (2018)
Bendsøe, M.P., Kikuchi, N.: Generating optimal topologies in structural design using a homogenization method. Comput. Methods Appl. Mech. Eng. 71(2), 197–224 (1988)
Bendsoe, M.P., Sigmund, O.: Topology optimization: theory, methods, and applications. Springer Science & Business Media (2003)
Borrvall, T., Petersson, J.: Topology optimization of fluids in stokes flow. Int. J. Numer. Meth. Fluids 41(1), 77–107 (2003)
Buhl, T., Pedersen, C.B.W., Sigmund, O.: Stiffness design of geometrically nonlinear structures using topology optimization. Struct. Multidiscip. Optim. 19(2), 93–104 (2000). https://doi.org/10.1007/s001580050089
Chi, H., et al.: Universal machine learning for topology optimization. Comput. Methods Appl. Mech. Eng. 375, 112739 (2021)
Cohen, T., Welling, M.: Group equivariant convolutional networks. In: International Conference on Machine Learning, pp. 2990–2999. PMLR (2016)
Dede, E.M.: Multiphysics topology optimization of heat transfer and fluid flow systems. In: Proceedings of the COMSOL Users Conference, vol. 715 (2009)
Deng, H., To, A.C.: Topology optimization based on deep representation learning (drl) for compliance and stress-constrained design. Comput. Mech. 66(2), 449–469 (2020)
Dittmer, S., Erzmann, D., Harms, H., Maass, P.: Selto: Sample-efficient learned topology optimization. arXiv preprint arXiv:2209.05098 (2022)
Dittmer, S., Erzmann, D., Harms, H., Falck, R., Gosch, M.: Selto dataset (2023). https://doi.org/10.5281/zenodo.7034898
Dühring, M.B., Jensen, J.S., Sigmund, O.: Acoustic design by topology optimization. J. Sound Vib. 317(3–5), 557–575 (2008)
Eschenauer, H.A., Olhoff, N.: Topology optimization of continuum structures: a review. Appl. Mech. Rev. 54(4), 331–390 (2001)
Ferguson, Z.: Topopt - topology optimization in python (2019). https://github.com/zfergus/topopt
Hoyer, S., Sohl-Dickstein, J., Greydanus, S.: Neural reparameterization improves structural optimization. arXiv preprint arXiv:1909.04240 (2019)
Hunter, W., et al.: Topy - topology optimization with python (2017). https://github.com/williamhunter/topy
Kingma, D.P., Ba, J.: Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980 (2014)
Lee, S., Kim, H., Lieu, Q.X., Lee, J.: Cnn-based image recognition for topology optimization. Knowl.-Based Syst. 198, 105887 (2020)
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. Design 143(3) (2021)
Paszke, A., et al.: Automatic differentiation in pytorch (2017)
Puny, O., Atzmon, M., Ben-Hamu, H., Smith, E.J., Misra, I., Grover, A., Lipman, Y.: Frame averaging for invariant and equivariant network design. arXiv preprint arXiv:2110.03336 (2021)
Qian, C., Ye, W.: Accelerating gradient-based topology optimization design with dual-model artificial neural networks. Struct. Multidiscip. Optim. 63(4), 1687–1707 (2021)
Ronneberger, O., Fischer, P., Brox, T.: U-Net: convolutional networks for biomedical image segmentation. In: Navab, N., Hornegger, J., Wells, W.M., Frangi, A.F. (eds.) MICCAI 2015. LNCS, vol. 9351, pp. 234–241. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24574-4_28
Sosnovik, I., Oseledets, I.: Neural networks for topology optimization. Russ. J. Numer. Anal. Math. Model. 34(4), 215–223 (2019)
Taubin, G.: Curve and surface smoothing without shrinkage. In: Proceedings of IEEE International Conference on Computer Vision, pp. 852–857. IEEE (1995)
Xue, L., Liu, J., Wen, G., Wang, H.: Efficient, high-resolution topology optimization method based on convolutional neural networks. Front. Mech. Eng. 16(1), 80–96 (2021). https://doi.org/10.1007/s11465-020-0614-2
Yoon, G.H., Jensen, J.S., Sigmund, O.: Topology optimization of acoustic-structure interaction problems using a mixed finite element formulation. Int. J. Numer. Meth. Eng. 70(9), 1049–1075 (2007)
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)
Zehnder, J., Li, Y., Coros, S., Thomaszewski, B.: Ntopo: Mesh-free topology optimization using implicit neural representations. Adv. Neural. Inf. Process. Syst. 34, 10368–10381 (2021)
Zhang, Y., Peng, B., Zhou, X., Xiang, C., Wang, D.: A deep convolutional neural network for topology optimization with strong generalization ability. arXiv preprint arXiv:1901.07761 (2019)
Zhang, Z., Li, Y., Zhou, W., Chen, X., Yao, W., Zhao, Y.: Tonr: An exploration for a novel way combining neural network with topology optimization. Comput. Methods Appl. Mech. Eng. 386, 114083 (2021)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Erzmann, D., Dittmer, S., Harms, H., Maaß, P. (2023). DL4TO : A Deep Learning Library for Sample-Efficient Topology Optimization. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2023. Lecture Notes in Computer Science, vol 14071. Springer, Cham. https://doi.org/10.1007/978-3-031-38271-0_54
Download citation
DOI: https://doi.org/10.1007/978-3-031-38271-0_54
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-38270-3
Online ISBN: 978-3-031-38271-0
eBook Packages: Computer ScienceComputer Science (R0)