[19] B. Bourdin and A. Chambolle. Design-dependent loads in topology optimization. ESAIM: Control, Optimisation and Calculus of Variations, 9:19-48, 2003.
[20] A. Brock, J. Donahue, and K. Simonyan. Large scale gan training for high fidelity natural image synthesis. arXiv preprint arXiv:1809.11096, 2018.
[21] T. B. Brown, B. Mann, N. Ryder, M. Subbiah, J. Kaplan, P. Dhariwal, A. Neelakantan, P. Shyam, G. Sastry, A. Askell, et al. Language models are few-shot learners. arXiv preprint arXiv:2005.14165, 2020.
[22] R. G. Budynas, J. K. Nisbett, et al. Shigley's mechanical engineering design, volume 9. McGraw-Hill New York, 2011.
[23] D. M. Buede and W. D. Miller. The engineering design of systems: models and methods. 2016.
[24] A. Chandrasekhar, S. Sridhara, and K. Suresh. Gm-tounn: Graded multiscale topology optimization using neural networks. arXiv preprint arXiv:2204.06682, 2022.
[25] A. Chandrasekhar and K. Suresh. Multi-material topology optimization using neural networks. Computer-Aided Design, 136:103017, 7 2021.
[26] H. Chen, K. S. Whitefoot, and L. B. Kara. Concurrent build direction, part segmentation, and topology optimization for additive manufacturing using neural networks. In International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, volume 86229, page V03AT03A029. American Society of Mechanical Engineers, 2022.
[27] R. Child. Very deep vaes generalize autoregressive models and can outperform them on images. arXiv preprint arXiv:2011.10650, 2020.
[28] J. Choi, S. Kim, Y. Jeong, Y. Gwon, and S. Yoon. Ilvr: Conditioning method for denoising diffusion probabilistic models. arXiv preprint arXiv:2108.02938, 2021.
[29] H. Deng and A. C. To. A parametric level set method for topology optimization based on deep neural network (dnn). Preprint, 1 2021.
[30] J. Devlin, M.-W. Chang, K. Lee, and K. Toutanova. Bert: Pre-training of deep bidirectional transformers for language understanding. arXiv preprint arXiv:1810.04805, 2018.
[31] P. Dhariwal and A. Nichol. Diffusion models beat gans on image synthesis. Advances in Neural Information Processing Systems, 34, 2021.
[32] M. O. Elingaard, N. Aage, J. A. Barentzen, and O. Sigmund. De-homogenization using convolutional neural networks. Computer Methods in Applied Mechanics and Engineering, 388:114197, 1 2022.
[33] L. C. Evans. Partial differential equations, volume 19. American Mathematical Society, 2022.
[34] A. Friedman. Partial differential equations of parabolic type. Courier Dover Publications, 2008.
[35] K. Fujita, K. Minowa, Y. Nomaguchi, S. Yamasaki, and K. Yaji. Design concept generation with variational deep embedding over comprehensive optimization. In International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-21, Virtual, Online, Aug 2021. ASME.
[36] P. Garabedian. Partial differential equations with more than two independent variables in the complex domain. Journal of Mathematics and Mechanics, pages 241-271, 1960.
[37] G. Giannone and F. Ahmed. Diffusing the optimal topology: A generative optimization approach. arXiv preprint arXiv:2303.09760, 2023.
[38] G. Giannone, D. Nielsen, and O. Winther. Few-shot diffusion models. arXiv preprint arXiv:2205.15463, 2022.
[39] J. K. Guest, J. H. Prevost, and T. Belytschko. Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International journal for numerical methods in engineering, 61(2):238-254, 2004.
[40] T. Guo, D. J. Lohan, R. Cang, M. Y. Ren, and J. T. Allison. 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, page 0804, 2018.