# Fileset [readme.pdf](https://mdr.nims.go.jp/filesets/ded8f5ce-2204-458c-acda-24180058c672/download) ## Creator [Xiaoyang Zheng](https://orcid.org/0000-0002-9004-9216), Ta-Te Chen, Xiaofeng Guo, Sadaki Samitsu, Ikumu Watanabe ## Rights [Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/) ## Other metadata [Tutorial for conditional generative adversarial network](https://mdr.nims.go.jp/datasets/14268605-d006-4212-b2d4-c2274ca555de) ## Fulltext Tutorial for conditional generative adversarial network Xiaoyang Zheng 1,2, Ikumu Watanabe 1,2 1 Graduate School of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba 305-8573, Japan 2 Research Center for Structural Materials, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba 305-0047, Japan Emails: ZHENG.Xiaoyang@nims.go.jp (X.Z.); WATANABE.Ikumu@nims.go.jp (I.W.) Abstract This tutorial aims to give an introduction of how to use a deep generative model, conditional generative adversarial network (CGAN). The CGAN can be used for the inverse design of 2D and 3D microstructures with target properties. The CGAN is trained with supervised learning using a labeled dataset. The dataset consists of a large number of geometries and their corresponding properties (e.g., elastic moduli). After training, the CGAN can generate a batch of geometries using target properties at inputs. In our previous two papers, we have demonstrated how to use the CGAN for the inverse design of 2D auxetic metamaterials and 3D architected materials [1,2]. We hope this tutorial can be useful for those who are interested in the inverse design problems of microstructures. 1. Introduction Figure 1. Forward design and inverse design mailto:ZHENG.Xiaoyang@nims.go.jpmailto:WATANABE.Ikumu@nims.go.jpForward design is a conventional approach to design microstructures, such as architected materials, mechanical metamaterials, lattices, etc. This forward design approach follows a general process: a structure is created firstly and then its mechanical properties are investigated by finite element simulation or mechanical testing (Figure 1). The mechanical properties of designed materials will be only known after time-consumingly simulations or experiments. In contrast, deep generative models, such as GAN, enable inverse design of microstructures. In inverse design, microstructures can be automatically generated by inputting target properties to a deep generative model, which outputs corresponding geometries of microstructures. Figure 2. Architecture of CGAN In our previous studies, we proposed an improved deep generative model, CGAN, for the inverse design of 2D auxetic metamaterials and 3D architected materials [1,2]. The CGAN is composed of three neural network structures: a generator, a discriminator, and a solver (Figure 2). The generator is trained to generate the realistic geometries from latent variables (multivariate normal distribution) and user-defined labels (target properties, e.g., elastic moduli), and simultaneously aims to deceive the discriminator and the solver. The discriminator is trained to distinguish geometries produced by the generator from the real dataset. The solver is trained to predict the properties of a given geometry. CGAN is optimized by a minimax game in the following equations: πœƒπœƒοΏ½π·π· = arg minπœƒπœƒπ·π·{𝐿𝐿𝐷𝐷�𝑑𝑑𝐷𝐷,𝐷𝐷(𝐗𝐗;πœƒπœƒπ·π·)οΏ½ + 𝐿𝐿𝐷𝐷(𝑒𝑒𝐷𝐷,𝐷𝐷(𝐺𝐺(𝐙𝐙,𝐋𝐋;πœƒπœƒπΊπΊ);πœƒπœƒπ·π·))} (1) πœƒπœƒοΏ½πΊπΊ = arg maxπœƒπœƒπ·π·{𝐿𝐿𝐷𝐷�𝑒𝑒𝐷𝐷,𝐷𝐷(𝐺𝐺(𝐙𝐙,𝐋𝐋; πœƒπœƒπΊπΊ);πœƒπœƒπ·π·)οΏ½ βˆ’ 𝛼𝛼 βˆ™ 𝐿𝐿𝑆𝑆(𝐿𝐿, 𝑆𝑆(𝐺𝐺(𝐙𝐙,𝐋𝐋; πœƒπœƒπΊπΊ);πœƒπœƒπ‘†π‘†))} (2) πœƒπœƒοΏ½π‘†π‘† = arg minπœƒπœƒπ‘†π‘†{𝐿𝐿𝑆𝑆�𝐿𝐿, 𝑆𝑆(𝐗𝐗;πœƒπœƒπ‘†π‘†)οΏ½} (3) Where πœƒπœƒπ·π·, πœƒπœƒπΊπΊ, πœƒπœƒπ‘†π‘† are sets of parameters of the discriminator, generator, and solver, respectively. D, G, and S denotes the discriminator, generator, and solver, respectively. 𝐗𝐗 ∈ ℝ𝑛𝑛×𝑝𝑝 is the training dataset (vectors of auxetic metamaterials), 𝐋𝐋 ∈ ℝ𝑛𝑛×𝑙𝑙 is the labels of the dataset X (i.e., Young’s moduli and Poisson’s ratios), and 𝐙𝐙 ∈ ℝ𝑛𝑛×𝑙𝑙 is latent variables from a multivariate normal distribution during each iteration. 𝐿𝐿𝐷𝐷 is a loss function (binary cross-entropy function) for the discriminator. 𝑑𝑑𝐷𝐷 and 𝑒𝑒𝐷𝐷 are target labels and generally set at as one and zero, respectively. (cSample generationGenerator objectDiscriminator objectSolver objectG(Z, L; ΞΈG) XZ (Noise) L (labels)Poisson’s ratioYoung’s modulusL (labels)Poisson’s ratioYoung’s modulusReal Fake RealGeneratorSolver DiscriminatorHowever, we apply label smoothing technique for the target labels: 𝑑𝑑𝐷𝐷 is replaced with a random number between 0.7 and 1.2, and 𝑒𝑒𝐷𝐷 is replaced with a random number between 0 and 0.3. The moderating weights, 𝛼𝛼, determines how much the generator focuses on the training of input labels, and is set to be 0.1 in our study. The deep learning calculations are performed using TensorFlow. Adam optimizer with learning rate of 0.0001 and Ξ²1 of 0.5 is used to train the model. The batch size for training is set to be 32. The detailed network structures used in this study are provided in Tables S1–S3. In short, the used layers include 2D convolutional layer, 2D transposed convolutional layer, 2D max pooling, fully connected layer, batch normalization, and dropout, and the used activation functions include leakyRELU and tanh. Note that circular padding is used in 2D convolutional layer and 2D transposed convolutional layer in order to keep and identify the periodicity of the patterns. Note that before using the CGAN, you need to prepare a labeled dataset consisting of 2D geometries and their corresponding properties (e.g., elastic moduli). The 2D geometries are represented using 2D images with shape of [b, 256, 256] and the properties are represented by two values with shape of [b, 2]. The letter β€œb” means the total number of geometries. The total number of geometries varies case by case, depending on the complexity and type of the geometries. In generally, the bigger the dataset, the better performance the training result. In our previous studies, we used 100,000 datapoints for 2D case and 10,000 datapoints for 3D case. The most convenient way is to generate geometries using code-based CAD modeling and calculate their properties using finite element simulations. 2. Procedures of CGAN training 2.1 Solver training As the solver is independent of the generator and discriminator, we firstly train the solver with supervised learning. Follow the steps below: a. Open solver.py with, e.g., PyCharm b. Change the source file in line 178 dataset_matrixes = np.load("yourdataset_geometries.npy"). The shape of β€œyourdataset_geometries.npy” should be [b,256,256]. b means the total number of geometries, and 256 means the height and width of a geometry image. β€œyourdataset_geometries.npy” consists of 0s and 1s, where 0 represents void part and 1 represents solid part. Note that the dataset will be divided with 80% for training and 20% for testing. (lines 182-185) The batch size is set to 32, and training epoch is 200. The comparison between the real and predicted values is plotted using line 221. The performance is investigated using the mean square error (MSE) of testing dataset using line 243. The check points (trained weights and biases) are saved using line 251. The check points will be used to train the generator and discriminator. 2.2 Generator and discriminator training After training the solver, we can use the saved weights of the solver to train the generator and discriminator. Follow the steps below: a. Open CGAN_main.py with, e.g., PyCharm b. Change the source file in line 292 dataset_matrixes = np.load("yourdataset_geometries.npy"). The shape of β€œyourdataset_geometries.npy” should be [b,256,256]. b means the total number of geometries, and 256 means the height and width of a geometry image. β€œyourdataset_geometries.npy” consists of 0s and 1s, where 0 represents void part and 1 represents solid part. c. Change the source file of saved weights in line 307 solver.load_weights(r"/ckpt/solver_199.ckpt") d. Change the limit of your dataspace in lines 289 and 290. For example, if your dataspace covers a square of [0,1], you can use current one. If not, e.g., a circle or triangle shape, you need to change the way to sample a datapoint from your dataspace. Note that the loss functions and MSE will be saved using lines 374-377. The weighs of the generator and the discriminator will be saved using lines 380 and 381. 2.3 Using trained CGAN for inverse design After training the solver, generator, and discriminator, we can use the saved weights of the solver and generator for the inverse design. Follow the steps below: a. Open generate_geometies_using_trained_cgan.py with, e.g., PyCharm b. Change the source file of saved weights of generator in line 145 generator.load_weights(r'ckpt/generator_199.ckpt') c. Change the source file of saved weights of solver in line 147 solver.load_weights(r"/ckpt/solver_199.ckpt") d. Change your target property for the condition in line 158 Note that the comparison between the input and output values will be save in the form of figures using line 171. The images of the generated 2D geometries will be saved using line 173. 3. Conclusions We give a tutorial of how to use CGAN for the inverse design of 2D geometries. After suitable training, the CGAN can take target properties as inputs and output corresponding 2D geometries. If you would like to use CGAN for the inverse design of 3D geometries, you can refer our latest paper [2], in which we proposed a 3D-CGAN that has a similar architecture with CGAN. If you meet any problems or have any comments, just feel free to contact us via emails. Hope you can enjoy our codes. Reference 1. Zheng X, Chen TT, Guo X, Samitsu S, Watanabe I. Controllable inverse design of auxetic metamaterials using deep learning. Materials & Design. 2021 Dec 1;211:110178. 2. Zheng X, Chen TT, Jiang X, Naito M, Watanabe I. Deep-learning-based inverse design of three-dimensional architected cellular materials with the target porosity and stiffness using voxelized Voronoi lattices. Science and Technology of Advanced Materials. 2023 Dec 31;24(1):2157682. Table S1: Network architecture of generator. Description Kernel size Resampling Input shape Output shape Concatenate(Z, L) - - 128+2 130 Fully connected + Batch Normalization + Reshape - - 130 4Γ—4Γ—512 2D Transposed convolution + Batch Normalization + Leaky ReLU 4Γ—4 Up 4Γ—4Γ—512 8Γ—8Γ—256 2D Transposed convolution + Batch Normalization + Leaky ReLU 4Γ—4 Up 8Γ—8Γ—256 16Γ—16Γ—128 2D Transposed convolution + Batch Normalization + Leaky ReLU 4Γ—4 Up 16Γ—16Γ—128 32Γ—32Γ—64 2D Transposed convolution + Batch Normalization + Leaky ReLU 4Γ—4 Up 32Γ—32Γ—64 64Γ—64Γ—32 2D Transposed convolution + Batch Normalization + Leaky ReLU 4Γ—4 Up 64Γ—64Γ—32 128Γ—128Γ—16 2D Transposed convolution 4Γ—4 Up 128Γ—128Γ—16 256Γ—256Γ—1 Tanh - - 256Γ—256Γ—1 256Γ—256Γ—1 Table S2: Network architecture of discriminator. Description Kernel size Resampling Input shape Output shape 2D convolution + Leaky ReLU + Dropout 4Γ—4 Down 256Γ—256Γ—1 128Γ—128Γ—16 2D convolution + Leaky ReLU + Dropout 4Γ—4 Down 128Γ—128Γ—16 64Γ—64Γ—32 2D convolution + Leaky ReLU + Dropout 4Γ—4 Down 64Γ—64Γ—32 32Γ—32Γ—64 2D convolution + Leaky ReLU + Dropout 4Γ—4 Down 32Γ—32Γ—64 16Γ—16Γ—128 2D convolution + Leaky ReLU + Dropout 4Γ—4 Down 16Γ—16Γ—128 8Γ—8Γ—256 2D convolution + Leaky ReLU + Dropout 4Γ—4 Down 8Γ—8Γ—256 4Γ—4Γ—512 Flatten - - 4Γ—4Γ—512 8192 Fully connected - - 8192 1 Table S3: Network architecture of solver. Description Kernel size / pool size Resampling Input shape Output shape Unit 1 2D convolution 3Γ—3 - 256Γ—256Γ—1 256Γ—256Γ—16 2D convolution 3Γ—3 - 256Γ—256Γ—16 256Γ—256Γ—16 2D Max pooling 2Γ—2 Down 256Γ—256Γ—1 128Γ—128Γ—16 Unit 2 2D convolution 3Γ—3 - 128Γ—128Γ—16 128Γ—128Γ—32 2D convolution 3Γ—3 - 128Γ—128Γ—32 128Γ—128Γ—32 2D Max pooling 2Γ—2 Down 128Γ—128Γ—32 64Γ—64Γ—32 Unit 3 2D convolution 3Γ—3 - 64Γ—64Γ—32 64Γ—64Γ—64 2D convolution 3Γ—3 - 64Γ—64Γ—64 64Γ—64Γ—64 2D Max pooling 2Γ—2 Down 64Γ—64Γ—64 32Γ—32Γ—64 Unit 4 2D convolution 3Γ—3 - 32Γ—32Γ—64 32Γ—32Γ—128 2D convolution 3Γ—3 - 32Γ—32Γ—128 32Γ—32Γ—128 2D Max pooling 2Γ—2 Down 32Γ—32Γ—128 16Γ—16Γ—128 Unit 5 2D convolution 3Γ—3 - 16Γ—16Γ—128 16Γ—16Γ—256 2D convolution 3Γ—3 - 16Γ—16Γ—256 16Γ—16Γ—256 2D Max pooling 2Γ—2 Down 16Γ—16Γ—256 8Γ—8Γ—256 Unit 6 2D convolution 3Γ—3 - 8Γ—8Γ—256 8Γ—8Γ—384 2D convolution 3Γ—3 - 8Γ—8Γ—384 8Γ—8Γ—384 2D Max pooling 2Γ—2 Down 8Γ—8Γ—384 4Γ—4Γ—384 Unit 7 2D convolution 3Γ—3 - 4Γ—4Γ—384 4Γ—4Γ—512 2D convolution 3Γ—3 - 4Γ—4Γ—512 4Γ—4Γ—512 2D Max pooling 2Γ—2 Down 4Γ—4Γ—512 2Γ—2Γ—512 Unit 8 2D convolution 3Γ—3 - 2Γ—2Γ—512 2Γ—2Γ—512 2D convolution 3Γ—3 - 2Γ—2Γ—512 2Γ—2Γ—512 2D Max pooling 2Γ—2 Down 2Γ—2Γ—512 1Γ—1Γ—512 Flatten + Fully connected - - 1Γ—1Γ—512 256 Fully connected 256 128 Fully connected - - 128 2 1. Introduction 2. Procedures of CGAN training 2.1 Solver training 2.2 Generator and discriminator training 2.3 Using trained CGAN for inverse design 3. Conclusions Reference