Katsuyuki Suzuki

Kazunari Wada, Katsuyuki Suzuki, Kazuo Yonekura

Generative adversarial networks (GAN) have recently been used for a design synthesis of mechanical shapes. A GAN sometimes outputs physically unreasonable shapes. For example, when a GAN model is trained to output airfoil shapes that indicate required aerodynamic performance, significant errors occur in the performance values. This is because the GAN model only considers data but does not consider the aerodynamic equations that lie under the data. This paper proposes the physics-guided training of the GAN model to guide the model to learn physical validity. Physical validity is computed using general-purpose software located outside the neural network model. Such general-purpose software cannot be used in physics-informed neural network frameworks, because physical equations must be implemented inside the neural network models. Additionally, a limitation of generative models is that the output data are similar to the training data and cannot generate completely new shapes. However, because the proposed model is guided by a physical model and does not use a training dataset, it can generate completely new shapes. Numerical experiments show that the proposed model drastically improves the accuracy. Moreover, the output shapes differ from those of the training dataset but still satisfy the physical validity, overcoming the limitations of existing GAN models.

Kazuo Yonekura, Kento Maruoka, Kyoku Tyou et al.

In a finite element analysis, using a large number of grids is important to obtain accurate results, but is a resource-consuming task. Aiming to real-time simulation and optimization, it is desired to obtain fine grid analysis results within a limited resource. This paper proposes a super-resolution method that predicts a stress tensor field in a high-resolution from low-resolution contour plots by utilizing a U-Net-based neural network which is called PI-UNet. In addition, the proposed model minimizes the residual of the equilibrium constraints so that it outputs a physically reasonable solution. The proposed network is trained with FEM results of simple shapes, and is validated with a complicated realistic shape to evaluate generalization capability. Although ESRGAN is a standard model for image super-resolution, the proposed U-Net based model outperforms ESRGAN model in the stress tensor prediction task.

Fu-Yao Ko, Katsuyuki Suzuki, Kazuo Yonekura

This paper proposes a novel reinforcement learning (RL) algorithm using improved Monte Carlo tree search (IMCTS) formulation for discrete optimum design of truss structures. IMCTS with multiple root nodes includes update process, the best reward, accelerating technique, and terminal condition. Update process means that once a final solution is found, it is used as the initial solution for next search tree. The best reward is used in the backpropagation step. Accelerating technique is introduced by decreasing the width of search tree and reducing maximum number of iterations. The agent is trained to minimize the total structural weight under various constraints until the terminal condition is satisfied. Then, optimal solution is the minimum value of all solutions found by search trees. These numerical examples show that the agent can find optimal solution with low computational cost, stably produces an optimal design, and is suitable for multi-objective structural optimization and large-scale structures.

Fu-Yao Ko, Katsuyuki Suzuki, Kazuo Yonekura

A novel method called mixed variable system Monte Carlo tree search (MVSMCTS) formulation is presented for optimization problems considering various types of variables with single and mixed continuous-discrete system. This method utilizes a reinforcement learning algorithm with improved Monte Carlo tree search (IMCTS) formulation. For sizing and shape optimization of truss structures, the design variables are the cross-sectional areas of the members and the nodal coordinates of the joints. MVSMCTS incorporates update process and accelerating technique for continuous variable and combined scheme for single and mixed system. Update process indicates that once a solution is determined by MCTS with automatic mesh generation in continuous space, it is used as the initial solution for next search tree. The search region should be expanded from the mid-point, which is the design variable for initial state. Accelerating technique is developed by decreasing the range of search region and the width of search tree based on the number of meshes during update process. Combined scheme means that various types of variables are coupled in only one search tree. Through several examples, it is demonstrated that this framework is suitable for mixed variable structural optimization. Moreover, the agent can find optimal solution in a reasonable time, stably generates an optimal design, and is applicable for practical engineering problems.

Kazuo Yonekura, Nozomu Miyamoto, Katsuyuki Suzuki

Machine learning models are recently utilized for airfoil shape generation methods. It is desired to obtain airfoil shapes that satisfies required lift coefficient. Generative adversarial networks (GAN) output reasonable airfoil shapes. However, shapes obtained from ordinal GAN models are not smooth, and they need smoothing before flow analysis. Therefore, the models need to be coupled with Bezier curves or other smoothing methods to obtain smooth shapes. Generating shapes without any smoothing methods is challenging. In this study, we employed conditional Wasserstein GAN with gradient penalty (CWGAN-GP) to generate airfoil shapes, and the obtained shapes are as smooth as those obtained using smoothing methods. With the proposed method, no additional smoothing method is needed to generate airfoils. Moreover, the proposed model outputs shapes that satisfy the lift coefficient requirements.