A deep learning–based method for the design of microstructural materials


Due to their designable properties, microstructural materials have emerged as an important class of materials that have the potential for used in a variety of applications. The design of such materials is challenged by the multifunctionality requirements and various constraints stemmed from manufacturing limitations and other practical considerations. Traditional design methods such as those based on topological optimization techniques rely heavily on high-dimensional physical simulations and can be inefficient. In addition, it is difficult to impose geometrical constraints in those methods. In this work, we propose a deep learning model based on deep convolutional generative adversarial network (DCGAN) and convolutional neural network (CNN) for the design of microstructural materials. The DCGAN is used to generate design candidates that satisfy geometrical constraints and the CNN is used as a surrogate model to link the microstructure to its properties. Once trained, the two networks are combined to form the design network which is utilized to for the inverse design. The advantages of the method include its high efficiency and the simplicity in handling geometrical constraints. In addition, no high-dimensional sensitivity simulations are required. The performance of the method is demonstrated on the design of microstructural materials with desired compliance tensor, subject to specified geometrical constraints.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23


  1. Abdel-Hamid O, Mohamed AR, Jiang H, Penn G (2012) Applying convolutional neural networks concepts to hybrid NN-HMM model for speech recognition. In Acoustics, Speech and Signal Processing (ICASSP), 2012 IEEE International Conference on (pp. 4277-4280). IEEE

  2. Arjovsky M, Chintala S, Bottou L (2017) Wasserstein generative adversarial networks. In International Conference on Machine Learning. pp. 214-223

  3. Bendsøe MP (1989) Optimal shape design as a material distribution problem. Structural optimization 1(4):193–202

    Article  Google Scholar 

  4. Bendsøe MP, Sigmund O (1999) Material interpolation schemes in topology optimization. Arch Appl Mech 69(9-10):635–654

    MATH  Article  Google Scholar 

  5. Bessa MA, Bostanabad R, Liu Z, Hu A, Apley DW, Brinson C, Liu WK (2017) A framework for data-driven analysis of materials under uncertainty: Countering the curse of dimensionality. Comput Methods Appl Mech Eng 320:633–667

    MathSciNet  MATH  Article  Google Scholar 

  6. Cang R, Li H, Yao H, Jiao Y, Ren Y (2018) Improving direct physical properties prediction of heterogeneous materials from imaging data via convolutional neural network and a morphology-aware generative model. Comput Mater Sci 150:212–221

    Article  Google Scholar 

  7. Chen W, Jeyaseelan A, Fuge M (2018) Synthesizing designs with inter-part dependencies using hierarchical generative adversarial networks. In: ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, ASME, Quebec City, Canada

  8. Fang N, Xi D, Xu J, Ambati M, Srituravanich W, Sun C, Zhang X (2006) Ultrasonic metamaterials with negative modulus. Nat Mater 5(6)

  9. Goodfellow I et al. (2014) Generative adversarial nets. In Advances in neural information processing systems: 2672-2680

  10. Guo X, Zhang W, Zhong W (2014) Doing topology optimization explicitly and geometrically—a new moving morphable components based framework. J Appl Mech 81(8):081009

    Article  Google Scholar 

  11. Guo T, Lohan DJ, Cang R, Ren MY, Allison JT (2018) An indirect design representation for topology optimization using variational autoencoder and style transfer. In: 2018 AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference 2018, p. 0804

  12. Gupta A, Cecen A, Goyal S, Singh AK, Kalidindi SR (2015) Structure–property linkages using a data science approach: application to a non-metallic inclusion/steel composite system. Acta Mater 91:239–254

    Article  Google Scholar 

  13. Hu X, Shen Y, Liu X, Fu R, Zi J (2004) Superlensing effect in liquid surface waves. Phys Rev E 69:030201

    Article  Google Scholar 

  14. Kingma DP, Ba J (2014) Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980

  15. Kodali N, Abernethy J, Hays J, Kira Z (2017) How to train your DRAGAN. arXiv preprint arXiv:1705.07215, 2(4)

  16. Krish S (2011) A practical generative design method. Comput Aided Des 43(1):88–100

    Article  Google Scholar 

  17. Krizhevsky A, Hinton G (2010) Convolutional deep belief networks on cifar-10. Unpublished manuscript, 40(7)

  18. Krizhevsky A, Sutskever I, Hinton GE (2012) Imagenet classification with deep convolutional neural networks. In Advances in neural information processing systems, pp. 1097-1105

  19. Lazarov BS, Wang F, Sigmund O (2016) Length scale and manufacturability in density-based topology optimization. Arch Appl Mech 86(1-2):189–218

    Article  Google Scholar 

  20. LeCun Y, Boser BE, Denker JS, Henderson D, Howard RE, Hubbard WE, Jackel LD (1990) Handwritten digit recognition with a back-propagation network. In Advances in neural information processing systems, pp. 396-404

  21. LeCun Y, Bottou L, Bengio Y, Haffner P (1998) Gradient-based learning applied to document recognition. Proc IEEE 86(11):2278–2324

    Article  Google Scholar 

  22. Ledig C, Theis L, Huszár F, Caballero J, Cunningham A, Acosta A, Shi W (2017) Photo-realistic single image super-resolution using a generative adversarial network. In CVPR Vol. 2, No. 3, p. 4

  23. Lei X, Liu C, Du Z, Zhang W, Guo X (2019) Machine learning-driven real-time topology optimization under moving morphable component-based framework. J Appl Mech 86(1):011004

    Article  Google Scholar 

  24. Li X, Yang Z, Brinson LC, Choudhary A, Agrawal A, Chen W (2018a) A deep adversarial learning methodology for designing microstructural material systems. In: ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2018, Paper No. DETC2018-85633, pp. V02BT03A008. American Society of Mechanical Engineers

  25. Li X, Zhang Y, Zhao H, Burkhart C, Brinson LC, Chen W (2018b) A transfer learning approach for microstructure reconstruction and structure-property predictions. Scientific reports, 8

  26. Liang B, Guo XS, Tu J, Zhang D, Chen JC (2010) An acoustic rectifier. Nat Mater 9:989–992

    Article  Google Scholar 

  27. Liu R, Yabansu YC, Agrawal A, Kalidindi SR, Choudhary AN (2015) Machine learning approaches for elastic localization linkages in high-contrast composite materials. Integrating Materials and Manufacturing Innovation 4(1):13

    Article  Google Scholar 

  28. Liu Q, Zhang N, Yang W, Wang S, Cui Z, Chen X, Chen L (2017) A review of image recognition with deep convolutional neural network. In International Conference on Intelligent Computing (pp. 69-80). Springer, Cham

  29. Lohan DJ, Dede EM, Allison JT (2017) Topology optimization for heat conduction using generative design algorithms. Struct Multidiscip Optim 55(3):1063–1077

    MathSciNet  Article  Google Scholar 

  30. Mao X, Li Q, Xie H, Lau RY, Wang Z, Smolley SP (2017) Least squares generative adversarial networks. In Computer Vision (ICCV), 2017 IEEE International Conference on (pp. 2813-2821). IEEE

  31. Martin GL (1993) Centered-object integrated segmentation and recognition of overlapping handprinted characters. Neural Comput 5(3):419–429

    Article  Google Scholar 

  32. McDowell DL, Olson GB (2008) Concurrent design of hierarchical materials and structures. Scientific Modeling and Simulations. Springer, Dordrecht, pp 207–240

    Google Scholar 

  33. Mirza M, Osindero S (2014) Conditional generative adversarial nets. arXiv preprint arXiv:1411.1784

  34. Nakshatrala P, Tortorelli D (2015) Topology optimization for effective energy propagation in rate-independent elastoplastic material systems. Comput Methods Appl Mech Eng 295:305–326

    MathSciNet  MATH  Article  Google Scholar 

  35. Osher SJ, Santosa F (2001) Level set methods for optimization problems involving geometry and constraints: I. frequencies of a two-density inhomogeneous drum. J Comput Phys 171(1):272–288

    MathSciNet  MATH  Article  Google Scholar 

  36. Radford A, Metz L, Chintala S (2015) Unsupervised representation learning with deep convolutional generative adversarial networks. arXiv preprint arXiv:1511.06434

  37. Reed S, Akata Z, Yan X, Logeswaran L, Schiele B, Lee H (2016) Generative adversarial text to image synthesis. arXiv preprint arXiv:1605.05396

  38. Rong J, Ye W (2019) Topology optimization design scheme for broadband non-resonant hyperbolic elastic metamaterials. Comput Methods Appl Mech Eng 344:819–836

    MathSciNet  MATH  Article  Google Scholar 

  39. Sosnovik I, Oseledets I (2017) Neural networks for topology optimization. arXiv preprint arXiv:1709.09578

  40. Vaz L, Hinton E (1995) FE-shape sensitivity of elastoplastic response. Struct Multidiscip Optim 10(3):231–238

    Article  Google Scholar 

  41. Villanueva CH, Maute K (2017) CutFEM topology optimization of 3D laminar incompressible flow problems. Comput Methods Appl Mech Eng 320:444–473

    MathSciNet  MATH  Article  Google Scholar 

  42. Wang SC (2003) Artificial neural network. In: Interdisciplinary computing in java programming. Springer, Boston, pp 81–100

    Google Scholar 

  43. Wang S, Wang MY (2006) Radial basis functions and level set method for structural topology optimization. Int J Numer Methods Eng 65(12):2060–2090

    MathSciNet  MATH  Article  Google Scholar 

  44. Wang MY, Wang X, Guo D (2003) A level set method for structural topology optimization. Comput Methods Appl Mech Eng 192(1-2):227–246

    MathSciNet  MATH  Article  Google Scholar 

  45. Yan F, Chan YC, Saboo A, Shah J, Olson GB, Chen W (2018) Data-driven prediction of mechanical properties in support of rapid certification of additively manufactured alloys. Comput Model Eng Sci:343–366

  46. Yang Z, Dai HM, Chan NH, Ma GC, Sheng P (2010) Acoustic metamaterial panels for sound attenuation in the 50-1000 Hz regime. Appl Phys Lett 96:041906

    Article  Google Scholar 

  47. Yu Y, Hur T, Jung J, Jang IG (2019) Deep learning for determining a near-optimal topological design without any iteration. Struct Multidiscip Optim 59(3):787–799

  48. Zeiler MD, Fergus R (2013) Stochastic pooling for regularization of deep convolutional neural networks. arXiv preprint arXiv:1301.3557

  49. Zhang Y, Ye W (2018) Deep learning based inverse method for layout design. Structural and Multidisciplinary Optimization: 1-10

  50. Zhang W, Zhou Y, Zhu J (2017) A comprehensive study of feature definitions with solids and voids for topology optimization. Comput Methods Appl Mech Eng 325:289–313

    MathSciNet  MATH  Article  Google Scholar 

  51. Zhao J, Mathieu M, LeCun Y (2016) Energy-based generative adversarial network. arXiv preprint arXiv:1609.03126

  52. Zhou Y, Zhang W, Zhu J, Xu Z (2016) Feature-driven topology optimization method with signed distance function. Comput Methods Appl Mech Eng 310:1–32

    MathSciNet  MATH  Article  Google Scholar 

  53. Zhu R, Liu XN, Hu GK, Sun CT, Huang GL (2014) Negative refraction of elastic waves at the deep-subwavelength scale in a single-phase metamaterials. Nat Commun 5:5510

    Article  Google Scholar 

Download references


This work is supported by the Hong Kong Research Grants under Competitive Earmarked Research Grant No. 16212318.

Author information



Corresponding author

Correspondence to Wenjing Ye.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Responsible Editor: Xu Guo

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Tan, R.K., Zhang, N.L. & Ye, W. A deep learning–based method for the design of microstructural materials. Struct Multidisc Optim 61, 1417–1438 (2020). https://doi.org/10.1007/s00158-019-02424-2

Download citation


  • Microstructural materials
  • Material design
  • Deep learning
  • Generative adversarial network
  • Convolutional neural network