Abstract
In this research, we propose a deep learning based approach for speeding up the topology optimization methods. The problem we seek to solve is the layout problem. The main novelty of this work is to state the problem as an image segmentation task. We leverage the power of deep learning methods as the efficient pixel-wise image labeling technique to perform the topology optimization. We introduce convolutional encoder-decoder architecture and the overall approach of solving the above-described problem with high performance. The conducted experiments demonstrate the significant acceleration of the optimization process. The proposed approach has excellent generalization properties. We demonstrate the ability of the application of the proposed model to other problems. The successful results, as well as the drawbacks of the current method, are discussed.
Funding: This study was supported by the Ministry of Education and Science of the Russian Federation (grant 14.756.31.0001).
References
[1] M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin et al., Tensorflow: Large-scale machine learning on heterogeneous distributed systems. arXiv preprint arXiv:1603.04467, 2016.Search in Google Scholar
[2] E. Andreassen, A. Clausen, M. Schevenels, B. S. Lazarov, and O. Sigmund, Efficient topology optimization in MATLAB using 88 lines of code. Struct. Multidiscip. Optimiz. 43 (2011), No. 1, 1–16.10.1007/s00158-010-0594-7Search in Google Scholar
[3] M. P. Bendsøe, Optimal shape design as a material distribution problem. Struct. Multidiscip. Optimiz. 1 (1989), No. 4, 193–202.10.1007/BF01650949Search in Google Scholar
[4] M. P. Bendsøe, Optimization of Structural Topology, Shape, and Material. Springer, 414, 1995.10.1007/978-3-662-03115-5Search in Google Scholar
[5] M. P. Bendsøe, E. Lund, N. Olhoff, and O. Sigmund, Topology optimization-broadening the areas of application. Control Cybern. 34 (2005), 7–35.Search in Google Scholar
[6] B. Bourdin, Filters in topology optimization. Int. J. Numer. Meth. Engrg. 50 (2001), No. 9, 2143–2158.10.1002/nme.116Search in Google Scholar
[7] G. Carleo and M. Troyer, Solving the quantum many-body problem with artificial neural networks. Science355 (2017), No. 6325, 602–606.10.1126/science.aag2302Search in Google Scholar
[8] F. Chollet et al, Keras. GitHub, 2015. URL: https://github.com/fchollet/keras.Search in Google Scholar
[9] K. Greff, R. M. J. van Damme, J. Koutnik, H. J. Broersma, J. Mikhal, C. P. Lawrence, W. G. van der Wiel, and J. Schmidhuber, Using neural networks to predict the functionality of reconfigurable nano-material networks. Int. J. Advances in Intelligent Systems9 (2017), No. 3–4, 339–351.Search in Google Scholar
[10] A. A. Groenwold and L. F. P. Etman, A simple heuristic for gray-scale suppression in optimality criterion-based topology optimization. Struct. Multidiscip. Optimiz. 39 (2009), No. 2, 217–225.10.1007/s00158-008-0337-1Search in Google Scholar
[11] W. Hunter et al., ToPy–Topology optimization with Python, 2017. URL: https://github.com/williamhunter/topy.Search in Google Scholar
[12] G. E. Hinton, N. Srivastava, A. Krizhevsky, I. Sutskever, and R. R. Salakhutdinov, Improving neural networks by preventing co-adaptation of feature detectors. arXiv preprint arXiv:1207.0580, 2012.Search in Google Scholar
[13] D. Kingma and J. Ba, Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014.Search in Google Scholar
[14] C. Mattheck and S. Burkhardt, A new method of structural shape optimization based on biological growth. Int. J. Fatigue12 (1990), No. 3, 185–190.10.1016/0142-1123(90)90094-USearch in Google Scholar
[15] K. Mills, M. Spanner, and I. Tamblyn, Deep learning and the Schrödinger equation. arXiv preprint arXiv:1702.01361, 2017.10.1103/PhysRevA.96.042113Search in Google Scholar
[16] H. P. Mlejnek, Some aspects of the genesis of structures. Struct. Multidiscip. Optimiz. 5 (1992), No. 1, 64–69.10.1007/BF01744697Search in Google Scholar
[17] M. Paganini, L. de Oliveira, and B. Nachman, CaloGAN: simulating 3D high energy particle showers in multi-layer electromagnetic calorimeters with generative adversarial networks. arXiv preprint arXiv:1705.02355, 2017.10.1103/PhysRevD.97.014021Search in Google Scholar
[18] O. Ronneberger, P. Fischer, and T. Brox, U-net: Convolutional networks for biomedical image segmentation. Int. Conf. on Medical Image Computing and Computer-Assisted Intervention. Springer, Munich, 2015, pp. 234–241.10.1007/978-3-319-24574-4_28Search in Google Scholar
[19] O. Sigmund, On the design of compliant mechanisms using topology optimization. J. Structural Mechanics25 (1997), No. 4, 493–524.10.1080/08905459708945415Search in Google Scholar
[20] O. Sigmund, A 99 line topology optimization code written in Matlab. Struct. Multidiscip. Optimiz. 21 (2001), No. 2, 120–127.10.1007/s001580050176Search in Google Scholar
[21] J. S. Smith, O. Isayev, and A. E. Roitberg, ANI-1: an extensible neural network potential with DFT accuracy at force field computational cost. Chemical Science8 (2017), No. 4, 3192–3203.10.1039/C6SC05720ASearch in Google Scholar
[22] K. Svanberg and H. Svärd, Density filters for topology optimization based on the Pythagorean means. Struct. Multidiscip. Optimiz. 48 (2013), No. 5, 859–875.10.1007/s00158-013-0938-1Search in Google Scholar
[23] J. Tompson, K. Schlachter, P. Sprechmann, and K.Perlin, Accelerating Eulerian fluid simulation with convolutional networks. arXiv preprint arXiv:1607.03597, 2016.Search in Google Scholar
[24] K. Um, X. Hu, and N. Thuerey, Liquid splash modeling with neural networks. arXiv preprint arXiv:1704.04456, 2017.10.1111/cgf.13522Search in Google Scholar
[25] Yi M. Xie and G. P. Steven, A simple evolutionary procedure for structural optimization. Computers&Structures49 (1993), No. 5, 885–896.10.1016/0045-7949(93)90035-CSearch in Google Scholar
© 2019 Walter de Gruyter GmbH, Berlin/Boston
