A Novel Topology Optimization Approach using Conditional Deep Learning

In this study, a novel topology optimization approach based on conditional Wasserstein generative adversarial networks (CWGAN) is developed to replicate the conventional topology optimization algorithms in an extremely computationally inexpensive way. CWGAN consists of a generator and a discriminator, both of which are deep convolutional neural networks (CNN). The limited samples of data, quasi-optimal planar structures, needed for training purposes are generated using the conventional topology optimization algorithms. With CWGANs, the topology optimization conditions can be set to a required value before generating samples. CWGAN truncates the global design space by introducing an equality constraint by the designer. The results are validated by generating an optimized planar structure using the conventional algorithms with the same settings. A proof of concept is presented which is known to be the first such illustration of fusion of CWGANs and topology optimization.

[1]  Jeffrey Dean,et al.  Distributed Representations of Words and Phrases and their Compositionality , 2013, NIPS.

[2]  Jun Wu,et al.  A System for High-Resolution Topology Optimization , 2016, IEEE Transactions on Visualization and Computer Graphics.

[3]  M. Zhou,et al.  Generalized shape optimization without homogenization , 1992 .

[4]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[5]  Ivan V. Oseledets,et al.  Neural networks for topology optimization , 2017, Russian Journal of Numerical Analysis and Mathematical Modelling.

[6]  Anders Clausen,et al.  Efficient topology optimization in MATLAB using 88 lines of code , 2011 .

[7]  Niels Olhoff,et al.  Topology optimization of continuum structures: A review* , 2001 .

[8]  Lawrence D. Jackel,et al.  Backpropagation Applied to Handwritten Zip Code Recognition , 1989, Neural Computation.

[9]  Ole Sigmund,et al.  A 99 line topology optimization code written in Matlab , 2001 .

[10]  Yu Li,et al.  Reconstruction of Simulation-Based Physical Field with Limited Samples by ReConNN , 2018, ArXiv.

[11]  Sergey Ioffe,et al.  Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift , 2015, ICML.

[12]  Nitish Srivastava,et al.  Dropout: a simple way to prevent neural networks from overfitting , 2014, J. Mach. Learn. Res..

[13]  Wojciech Zaremba,et al.  Improved Techniques for Training GANs , 2016, NIPS.

[14]  Léon Bottou,et al.  Wasserstein GAN , 2017, ArXiv.

[15]  Soumith Chintala,et al.  Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks , 2015, ICLR.

[16]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.

[17]  Christian Ledig,et al.  Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network , 2016, 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[18]  Sun Yong Kim,et al.  A new efficient convergence criterion for reducing computational expense in topology optimization: reducible design variable method , 2012 .

[19]  Yu-Lun Chiu,et al.  Dynamic modeling of batch polymerization reactors via the hybrid neural-network rate-function approach , 2007 .

[20]  Martin P. Bendsøe,et al.  Optimization of Structural Topology, Shape, And Material , 1995 .

[21]  Yonggyun Yu,et al.  Deep learning for topology optimization design , 2018, ArXiv.

[22]  Hai Yang,et al.  Exploration of route choice behavior with advanced traveler information using neural network concepts , 1993 .

[23]  M. Bendsøe Optimal shape design as a material distribution problem , 1989 .

[24]  Simon Osindero,et al.  Conditional Generative Adversarial Nets , 2014, ArXiv.

[25]  Michel Cabassud,et al.  Elaboration of a neural network system for semi-batch reactor temperature control: an experimental study , 1996 .

[26]  Mostafa Langarizadeh,et al.  A novel method for fuzzy diagnostic system design , 2018, Medical journal of the Islamic Republic of Iran.

[27]  Yoshua Bengio,et al.  Generative Adversarial Networks , 2014, ArXiv.

[28]  Adarsh Krishnamurthy,et al.  A Machine-Learning Framework for Design for Manufacturability , 2017, ArXiv.

[29]  Duane Detwiler,et al.  Towards Nonlinear Multimaterial Topology Optimization Using Unsupervised Machine Learning and Metamodel-Based Optimization , 2015, DAC 2015.

[30]  In Gwun Jang,et al.  Deep learning for determining a near-optimal topological design without any iteration , 2018, Structural and Multidisciplinary Optimization.