Combined sizing and layout optimization of truss structures via update Monte Carlo tree search (UMCTS) algorithm

The main concern of this study is to find the optimal design of truss structures considering sizing and layout variables simultaneously. As compared to purely sizing optimization problems, this problem is more challenging since the two types of variables involved are fundamentally different in nature. In this paper, a reinforcement learning method combining the update process and Monte Carlo tree search called the update Monte Carlo tree search (UMCTS) for sizing optimization problems is applied to solve combined sizing and layout optimization for truss structures. This study proposes a novel update process for nodal coordinates with two features. (1) The allowed range of each coordinate varies in each round. (2) Accelerators for the number of entries in the allowed range and iteration numbers are introduced to reduce the computation time. Furthermore, nodal coordinates and member areas are determined at the same time with only one search tree in each round. The validation and efficiency of the UMCTS are tested on benchmark problems of planar and spatial trusses with discrete sizing variables and continuous layout variables. It is shown that the CPU time of the UMCTS is two times faster than the branch and bound method. The numerical results demonstrate that the proposed method stably achieves a better solution than other traditional methods.

Update Monte Carlo tree search algorithm for heuristic global search of sizing optimization problems for truss structures

Sizing optimization of truss structures is a complex computational problem, and the reinforcement learning (RL) is suitable for dealing with multimodal problems without gradient computations. In this paper, a new efficient optimization algorithm called update Monte Carlo tree search (UMCTS) is developed to obtain the appropriate design for truss structures. UMCTS is an RL-based method that combines the novel update process and Monte Carlo tree search (MCTS) with the upper confidence bound (UCB). Update process means that in each round, the optimal cross-sectional area of each member is determined by search tree, and its initial state is the final state in the previous round. In the UMCTS algorithm, an accelerator for the number of selections for member area and iteration number is introduced to reduce the computation time. Moreover, for each state, the average reward is replaced by the best reward collected on the simulation process to determine the optimal solution. The proposed optimization method is examined on some benchmark problems of planar and spatial trusses with discrete sizing variables to demonstrate the efficiency and validity. It is shown that the computation time for the proposed approach is at least ten times faster than the branch and bound (BB) method. The numerical results indicate that the proposed method stably achieves better solution than other conventional methods.

Physics-guided training of GAN to improve accuracy in airfoil design synthesis

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.

Physics-guided generative adversarial network to learn physical models

This short note describes the concept of guided training of deep neural networks (DNNs) to learn physically reasonable solutions. DNNs are being widely used to predict phenomena in physics and mechanics. One of the issues of DNNs is that their output does not always satisfy physical equations. One approach to consider physical equations is adding a residual of equations into the loss function; this is called physics-informed neural network (PINN). One feature of PINNs is that the physical equations and corresponding residual must be implemented as part of a neural network model. In addition, the residual does not always converge to a small value. The proposed model is a physics-guided generative adversarial network (PG-GAN) that uses a GAN architecture in which physical equations are used to judge whether the neural network's output is consistent with physics. The proposed method was applied to a simple problem to assess its potential usability.

Super-resolving 2D stress tensor field conserving equilibrium constraints using physics informed U-Net

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.

Inverse airfoil design method for generating varieties of smooth airfoils using conditional WGAN-gp

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.