Skip to main content
SpringerLink
Log in

DL4TO : A Deep Learning Library for Sample-Efficient Topology Optimization

  • Conference paper
  • First Online:
Geometric Science of Information (GSI 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14071))

Included in the following conference series:

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The DL4TO library is publicly available at https://github.com/dl4to/dl4to.

References

  1. 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)

    Article  MathSciNet  Google Scholar 

  2. Abueidda, D.W., Koric, S., Sobh, N.A.: Topology optimization of 2d structures with nonlinearities using deep learning. Comput. Structures 237, 106283 (2020)

    Article  Google Scholar 

  3. Banga, S., Gehani, H., Bhilare, S., Patel, S., Kara, L.: 3d topology optimization using convolutional neural networks. arXiv preprint arXiv:1808.07440 (2018)

  4. 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)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bendsoe, M.P., Sigmund, O.: Topology optimization: theory, methods, and applications. Springer Science & Business Media (2003)

    Google Scholar 

  6. Borrvall, T., Petersson, J.: Topology optimization of fluids in stokes flow. Int. J. Numer. Meth. Fluids 41(1), 77–107 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  7. 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

    Article  Google Scholar 

  8. Chi, H., et al.: Universal machine learning for topology optimization. Comput. Methods Appl. Mech. Eng. 375, 112739 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  9. Cohen, T., Welling, M.: Group equivariant convolutional networks. In: International Conference on Machine Learning, pp. 2990–2999. PMLR (2016)

    Google Scholar 

  10. Dede, E.M.: Multiphysics topology optimization of heat transfer and fluid flow systems. In: Proceedings of the COMSOL Users Conference, vol. 715 (2009)

    Google Scholar 

  11. 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)

    Article  MathSciNet  MATH  Google Scholar 

  12. Dittmer, S., Erzmann, D., Harms, H., Maass, P.: Selto: Sample-efficient learned topology optimization. arXiv preprint arXiv:2209.05098 (2022)

  13. Dittmer, S., Erzmann, D., Harms, H., Falck, R., Gosch, M.: Selto dataset (2023). https://doi.org/10.5281/zenodo.7034898

  14. Dühring, M.B., Jensen, J.S., Sigmund, O.: Acoustic design by topology optimization. J. Sound Vib. 317(3–5), 557–575 (2008)

    Article  Google Scholar 

  15. Eschenauer, H.A., Olhoff, N.: Topology optimization of continuum structures: a review. Appl. Mech. Rev. 54(4), 331–390 (2001)

    Article  Google Scholar 

  16. Ferguson, Z.: Topopt - topology optimization in python (2019). https://github.com/zfergus/topopt

  17. Hoyer, S., Sohl-Dickstein, J., Greydanus, S.: Neural reparameterization improves structural optimization. arXiv preprint arXiv:1909.04240 (2019)

  18. Hunter, W., et al.: Topy - topology optimization with python (2017). https://github.com/williamhunter/topy

  19. Kingma, D.P., Ba, J.: Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980 (2014)

  20. Lee, S., Kim, H., Lieu, Q.X., Lee, J.: Cnn-based image recognition for topology optimization. Knowl.-Based Syst. 198, 105887 (2020)

    Article  Google Scholar 

  21. 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)

    Google Scholar 

  22. Paszke, A., et al.: Automatic differentiation in pytorch (2017)

    Google Scholar 

  23. 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)

  24. Qian, C., Ye, W.: Accelerating gradient-based topology optimization design with dual-model artificial neural networks. Struct. Multidiscip. Optim. 63(4), 1687–1707 (2021)

    Article  MathSciNet  Google Scholar 

  25. 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

    Chapter  Google Scholar 

  26. Sosnovik, I., Oseledets, I.: Neural networks for topology optimization. Russ. J. Numer. Anal. Math. Model. 34(4), 215–223 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  27. Taubin, G.: Curve and surface smoothing without shrinkage. In: Proceedings of IEEE International Conference on Computer Vision, pp. 852–857. IEEE (1995)

    Google Scholar 

  28. 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

    Article  Google Scholar 

  29. 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)

    Article  MathSciNet  MATH  Google Scholar 

  30. 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)

    Article  Google Scholar 

  31. 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)

    Google Scholar 

  32. 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)

  33. 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)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Industrial Mathematics, University of Bremen, Bremen, Germany

    David Erzmann, Sören Dittmer, Henrik Harms & Peter Maaß

  2. Cambridge Image Analysis, Centre for Mathematical Sciences, University of Cambridge, Cambridge, UK

    Sören Dittmer

Authors
  1. David Erzmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sören Dittmer
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Henrik Harms
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Peter Maaß
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to David Erzmann .

Editor information

Editors and Affiliations

  1. Sony Computer Science Laboratories Inc., Tokyo, Japan

    Frank Nielsen

  2. THALES Land and Air Systems, Meudon, France

    Frédéric Barbaresco

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

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)

Publish with us

Policies and ethics

Search

Navigation