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Structural reliability analysis, when accounting for non-parameterized probability box (P-box) uncertainty, typically entails multiple calls to performance functions and poses significant computational hurdles, largely attributable to its inherently nested double-loop structure. Therefore, this paper proposes a new reliability analysis method tailored for structures with uncertain parameters represented using non-parameterized P-boxes. This method leverages double-loop deep learning models to efficiently calculate both the upper and lower bounds of the failure probability. In the development phase of the double-loop deep learning model, an active learning function is devised that integrates the local prediction uncertainty of the deep learning model, based on the K-fold cross-validation principle with the proximity of training samples to candidate sample points. Different stopping criteria are formulated at distinct stages of the model construction process. Firstly, within the inner loop, a deep learning model is established to represent the original performance function in relation to the input parameters. Secondly, based on the inner-loop deep learning model for the performance function, an outer-loop deep learning model is established for the auxiliary response function corresponding to the P-box bound curves of the performance function response with respect to standard uniform distribution variables. Thirdly, utilizing the outer-loop deep learning approximate model, the Monte Carlo simulation technique is employed to compute the upper and lower bounds of the structural failure probability. Finally, the effectiveness of the proposed method is validated through the investigation of two numerical examples and a practical engineering problem. The influence of parameters in the active learning function, threshold values for stopping criteria, and the number of sample points on the computational results is deliberated. [ABSTRACT FROM AUTHOR]

Rapid advancement in additive manufacturing capabilities and computational resources has catalyzed multiscale topology optimization (TO). Recently, TO in general and multiscale TO in particular have received increased attraction due to its systematic approach to design globally and locally optimized structures. The multiscale TO computational paradigm brings additional new challenges, including geometric frustration, non-smooth boundaries, and higher computational time that needs to be handled. In this paper, a novel deep learning-based computational pipeline is developed to overcome the challenges encountered in the multiscale TO framework. The outlined computational pipeline employs two neural networks (NNs) architecture: (1) SILONet and (2) ConnectivetyNet. SILONet predicts optimized microstructure for elements of macroscale optimized structure, and ConnectivetyNet improves connectivity for multiscale topology fitted with SILONet outputs. The main novelty of this paper is the utilization of two NNs architecture for alleviating challenges, such as geometric frustration, non-smooth edges, dangling structures at boundaries, and accelerating multiscale TO computations while capturing essential physics and ensuring optimized solutions. The effectiveness of the proposed approach is demonstrated by its application to several two-dimensional and three-dimensional test cases. [ABSTRACT FROM AUTHOR]

Machine Learning (ML) techniques have been used in an extensive range of applications in the field of structural and multidisciplinary optimization over the last few years. This paper presents a survey of this wide but disjointed literature on ML techniques in the structural and multidisciplinary optimization field. First, we discuss the challenges associated with conventional optimization and how Machine learning can address them. Then, we review the literature in the context of how ML can accelerate design synthesis and optimization. Some real-life engineering applications in structural design, material design, fluid mechanics, aerodynamics, heat transfer, and multidisciplinary design are summarized, and a brief list of widely used open-source codes as well as commercial packages are provided. Finally, the survey culminates with some concluding remarks and future research suggestions. For the sake of completeness, categories of ML problems, algorithms, and paradigms are presented in the Appendix. [ABSTRACT FROM AUTHOR]

In this paper, a cross-resolution acceleration method for topology optimization is proposed based on deep learning aiming at achieving precise and high-efficiency geometrically non-linear structure design. We develop a cross-resolution Pix2pix neural network (CR-Pix2pix NN) to build the high-dimensional mapping between the low-resolution intermediate configuration (IC) and the corresponding high-resolution optimized configuration. Architecture of CR-Pix2pix NN is composed of a cross-resolution generator and Markovian discriminator. The cross-resolution geometrically non-linear dataset utilized to train the deep learning model is created by solving stress constrained topology optimization model established by independent continuous mapping (ICM) method. The pre-trained CR-Pix2pix NN is capable of accurately predicting the high-resolution optimized configuration by inputting the low-resolution IC with the only one iteration step. Furthermore, the hyperparameters of the developed model are discussed to ensure the performance in accuracy and computational efficiency. The proposed method can be generalized to other precise topology optimization scenarios and engineering design. [ABSTRACT FROM AUTHOR]

Topology optimization is computationally demanding for times of finite element analysis during iteration, especially for 3D structure optimization in intelligent design and construction, where a large amount of concept designs are executed. To this end, this paper proposes a deep Convolutional Neural Network (CNN) for 3D structural topology optimization, which can predict a near-optimal structure in negligible time without using any iterative scheme. To train the neural network, the Simplified Isotropic Material with Penalization (SIMP) method was adopted to generate the dataset of the optimized structures under the randomness loading conditions and volume fractions. The performance evaluation results show that compared with the SIMP method, the proposed method achieved a significant reduction in computation cost with little sacrifice on the performance of design solutions. Furthermore, the generalization ability of the proposed method trained on single boundary condition as well as multiple boundary conditions are explored. Finally, a stress-based topology optimization of the L-shape design domain is performed, which shows the portability of the proposed method to other more complex constraints. [ABSTRACT FROM AUTHOR]

In this paper, a simple deep learning network (DLN) based on the geometry parameters of moving morphable bars (MMBs) was proposed for the data-driven optimal topology prediction. The MMBs-based topology optimization approach is adopted to generate datasets that contain optimized topologies described by the geometry parameters. The DLN is simply built based on linear regression using a rectified linear unit (ReLU) activation function to minimize the loss function, which can be measured by the mean square error of the geometry parameters. The proposed approach could instantaneously provide an appropriate topology optimization design once the DLN has been trained. This approach does not require finite element analysis, design variable update, and other computations (e.g., sensitivity analysis) as often seen in the existing topology optimization approaches. Compared to the DLN based on element densities, the number of design variables and training time can be reduced significantly; the gray elements in void zones can also be also discarded. [ABSTRACT FROM AUTHOR]

Layout design is encountered in many fields of engineering and science. Those with complex constraints are particularly challenging to solve due to the non-uniqueness of the solution and the difficulties in incorporating the constraints into the conventional optimization-based methods. In this paper, we propose a design method based on the recently developed machine learning technique, variational autoencoder (VAE). We utilize the learning capability of the VAE to learn the constraints and the generative capability of the VAE to generate design candidates that automatically satisfy all the constraints. As such, no constraints need to be imposed during the design stage. In addition, we show that the VAE network is also capable of learning the underlying physics of the design problem, leading to an efficient design tool that does not need any physical simulation once the network is constructed. We demonstrated the performance of the method on two cases: inverse design of surface diffusion–induced morphology change and mask design for optical microlithography. [ABSTRACT FROM AUTHOR]

This paper introduces a novel deep learning approach for generating fine resolution structures that preserve all the information from the topology optimization (TO). The proposed approach utilizes neural networks (NNs) that map the desired engineering properties to seed for determining optimized structure. The main novelty of this framework is the utilization of parameters such as density and nodal deflections to predict optimized topologies for a wide range of design space. In this research, a three-stage NN framework is employed, wherein the first stage is a feedforward deep neural network. The second stage uses a convolutional neural network (CNN), and the final stage is the post-processing of results obtained from CNN. The first stage maps input design variables vector to output density distribution image. The image output of the first stage and design variables vector inputted to the first network serve as inputs to the second stage, which outputs optimized structure. Finally, post-processing of this optimized structure is done to ensure volume fraction constraint and optimal solution. These structures can be tessellated per the nodal displacement of an FEA solved larger structure. Because of this framework, the proposed approach makes TO computations faster and captures essential physics while using NNs to determine the final structure. The application of the proposed model to three-dimensional problems is also demonstrated. [ABSTRACT FROM AUTHOR]

Concurrent multiscale structural optimization is concerned with the improvement of macroscale structural performance through the design of microscale architectures. The multiscale design space must consider variables at both scales, so design restrictions are often necessary for feasible optimization. This work targets such design restrictions, aiming to increase microstructure complexity through deep learning models. The deep neural network (DNN) is implemented as a model for both microscale structural properties and material shape derivatives (shape sensitivity). The DNN’s profound advantage is its capacity to distill complex, multidimensional functions into explicit, efficient, and differentiable models. When compared to traditional methods for parameterized optimization, the DNN achieves sufficient accuracy and stability in a structural optimization framework. Through comparison with interface-aware finite element methods, it is shown that sufficiently accurate DNNs converge to produce a stable approximation of shape sensitivity through back propagation. A variety of optimization problems are considered to directly compare the DNN-based microscale design with that of the Interface-enriched Generalized Finite Element Method (IGFEM). Using these developments, DNNs are trained to learn numerical homogenization of microstructures in two and three dimensions with up to 30 geometric parameters. The accelerated performance of the DNN affords an increased design complexity that is used to design bio-inspired microarchitectures in 3D structural optimization. With numerous benchmark design examples, the presented framework is shown to be an effective surrogate for numerical homogenization in structural optimization, addressing the gap between pure material design and structural optimization. [ABSTRACT FROM AUTHOR]

Topology optimization (TO) provides a systematic approach for obtaining structure design with optimum performance of interest. However, the process requires the numerical evaluation of the objective function and constraints at each iteration, which is computationally expensive, especially for large-scale designs. Deep learning-based models have been developed to accelerate the process either by acting as surrogate models replacing the simulation process, or completely replacing the optimization process. However, most of them require a large set of labelled training data, which is generated mostly through simulations. The data generation time scales rapidly with the design size, decreasing the efficiency of the method itself. Another major issue is the weak generalizability of deep learning models. Most models are trained to work with the design problem similar to that used for data generation and require retraining if the design problem changes. In this work an adaptive, scalable deep learning-based model-order-reduction method is proposed to accelerate large-scale TO process, by utilizing MapNet, a neural network which maps the field of interest from coarse-scale to fine-scale. The proposed method allows for each simulation of the TO process to be performed at a coarser mesh, thereby greatly reducing the total computational time. More importantly, a crucial element, domain fragmentation, is introduced and integrated into the method, which greatly improves the transferability and scalability of the method. It has been demonstrated that the MapNet trained using data from one cantilever beam design with a specific loading condition can be directly applied to other structure design problems with different domain shapes, sizes, boundary and loading conditions. [ABSTRACT FROM AUTHOR]

Manipulating the distribution of functional particles in a polymer matrix can enable the fabrication of multifunctional smart composite devices. Using an acoustic field for particle patterning is a promising technique to alleviate the need for electrically conductive particles or magnetically responsive particles. To better understand the acoustic particle patterning process, a 3D high-fidelity multiphysics model is generally utilized. However, thousands of forward simulations are often required to determine a suitable set of input parameters for a desired particle pattern. It is advantageous to replace the computationally expensive forward simulation model with a cheaper-to-evaluate surrogate model to optimize the acoustic particle patterning process. This work develops a physics-informed machine learning approach to build a surrogate model capable of predicting the acoustic pressure pattern, which is highly related to the particle pattern. The surrogate model has an encoder–decoder structure, and the model training uses simulation data generated from a 3D multiphysics model. The multiphysics model is validated against experimental data before the generation of the simulation data. Physical knowledge is incorporated into the encoder–decoder model through a physics-informed input derived from the output of a 2D multiphysics model. This 2D model is constructed based on a cut plane of the 3D model to preserve most of the acoustic pressure information from the complex 3D model while being more efficient to evaluate and suitable for online prediction. The proposed physics-informed encoder–decoder model can increase the quality of the acoustic pattern prediction by over 40% compared to the base encoder–decoder model. Incorporating the physics-informed input into the base encoder–decoder can significantly reduce the sample size and model complexity required for achieving a given acoustic pattern prediction accuracy. This work provides a guideline for developing physics-informed machine learning models for manufacturing processes. [ABSTRACT FROM AUTHOR]

The braking performance of the brake system is a target performance that must be considered for vehicle development. Apparent piston travel (APT) and drag torque are the most representative factors for evaluating braking performance. In particular, as the two performance factors have a conflicting relationship with each other, a multidisciplinary design optimization (MDO) approach is required for brake design. However, the computational cost of MDO increases as the number of disciplines increases. Recent studies on inverse design that use deep learning (DL) have established the possibility of instantly generating an optimal design that can satisfy the target performance without implementing an iterative optimization process. This study proposes a DL-based multidisciplinary inverse design (MID) that simultaneously satisfies multiple targets, such as the APT and drag torque of the brake system. Results show that the proposed inverse design can find the optimal design more efficiently compared with the conventional optimization methods, such as backpropagation and sequential quadratic programming. The MID achieved a similar performance to the single-disciplinary inverse design in terms of accuracy and computational cost. A novel design was derived on the basis of results, and the same performance was satisfied as that of the existing design. [ABSTRACT FROM AUTHOR]

The present study analyzes the thermal attribute of conductive, convective, and radiative moving fin with thermal conductivity and constant velocity. The basic Darcy’s model is utilized to formulate the governing equation for the problem, which is further nondimensionalized using certain variables. Moreover, an effective soft computing paradigm based on the approximating ability of the feedforword artificial neural networks (FANN’s) and meta-heuristic approach of global and local search optimization techniques is developed to quantify the effect of variations in significant parameters such as ambient temperature, radiation-conduction number, Peclet number, nonconstant thermal conductivity, and initial temperature parameter on the temperature gradient of the rod. The results by the proposed FANN-AOA-SQP algorithm are compared with radial basis function approximation, Runge–Kutta–Fehlberg method and machine-learning algorithms. An extensive graphical and statistical analysis based on solution curves and errors such as absolute errors, mean square error, standard deviations in Nash–Sutcliffe efficiency, mean absolute deviations, and Theil’s inequality coefficient are performed to show the accuracy, ease of implementation, and robustness of the design scheme. [ABSTRACT FROM AUTHOR]

Injection molding is one of the most popular manufacturing methods for making complex plastic objects. Faster numerical simulation of this manufacturing process would allow faster and cheaper design cycles of new products. In this work, we propose a data processing pipeline that includes the extraction of data from Moldflow simulation projects and the prediction of the fill time and deflection distributions over 3-dimensional surfaces using machine learning models. We propose algorithms for the engineering of features, including information of injector gates parameters that will mostly affect the time for plastic to reach the particular point of the form for fill time prediction, and geometrical features for deflection prediction. We propose and evaluate machine learning models for fill time and deflection distribution prediction and provide values of Mean Absolute Error, Median Absolute Error, and Root Mean Square Error metrics. Finally, we measure the execution time of our solution and show that our solution is much faster than Moldflow: approximately, 17 times and 14 times faster for mean and median total times, respectively, comparing the times of all analysis stages for deflection prediction. Our solution has been implemented in a prototype web application that was approved by the management board of Fiat Chrysler Automobiles and Illogic SRL. As one of the promising applications of similar surrogate modeling approaches, we envision the use of trained models as a fast objective function for optimizing injection molding process parameters, such as optimal placement of gates, which could significantly aid engineers in this task, or even automate it. [ABSTRACT FROM AUTHOR]

The question of how methods from the field of artificial intelligence can help improve the conventional frameworks for topology optimisation has received increasing attention over the last few years. Motivated by the capabilities of neural networks in image analysis, different model-variations aimed at obtaining iteration-free topology optimisation have been proposed with varying success. Other works focused on speed-up through replacing expensive optimisers and state solvers, or reducing the design-space have been attempted, but have not yet received the same attention. The portfolio of articles presenting different applications has as such become extensive, but few real breakthroughs have yet been celebrated. An overall trend in the literature is the strong faith in the “magic”of artificial intelligence and thus misunderstandings about the capabilities of such methods. The aim of this article is therefore to present a critical review of the current state of research in this field. To this end, an overview of the different model-applications is presented, and efforts are made to identify reasons for the overall lack of convincing success. A thorough analysis identifies and differentiates between problematic and promising aspects of existing models. The resulting findings are used to detail recommendations believed to encourage avenues of potential scientific progress for further research within the field. [ABSTRACT FROM AUTHOR]

Determination of regional deteriorating bridges’ maintenance strategies for minimizing life-cycle risks and costs constructs a complex optimization problem. Improper maintenance strategies lead to budget waste and ineffective maintenances. To optimize the life-cycle maintenance strategies of regional bridges, this study develops a deep reinforcement learning (DRL)-based framework to enable the agent to learn better maintenance actions in an interactive environment by trial and error. It is able to generate several optimal maintenance strategies to match with different budget constraints under the premise of increasing the maintenance cost-effectiveness to the greatest extent possible. The framework contains the whole optimization process from data collection to regional functions establishment to reinforcement learning training. The regional structural deterioration features and the effect of maintenance actions are determined by years of regional inspection reports. The regional probabilistic models are incorporated to simulate the stochastic process. The regional life-cycle maintenance strategies are optimized with the deep Q-networks model. The proposed framework is substantiated by developing 100-year maintenance strategies for part of highway bridges. The results show that the trained optimal maintenance strategies match well with the given budget constraints and maximize the life-cycle cost-effectiveness of maintenance actions. By employing the trained maintenance strategies, the conditions of regional bridges are controlled at a good level. Besides, the trained optimal DRL-based strategies have better performance than traditional condition-fixed strategies. [ABSTRACT FROM AUTHOR]

Rapid development in deep learning methods has brought about wide applications of artificial-neural-network (ANN)-based surrogate models in the field of numerical simulation. Given sufficient training, ANN-based surrogate models can be both accurate and efficient, and thus can be used to replace computationally expensive numerical simulations in problems where intensive numerical simulations are required. However, the training of ANN-based surrogate models relies on a large corpus of ground-truth data that is often generated using full-scale numerical simulations. For such large-scale problems, the computational cost of generating training data can be massive which diminishes the efficiency gained using ANN-based surrogate models and limits their application scope. In this work, a solution scheme is proposed to address this issue by reducing the full-scale numerical simulations needed during training data generation, thus reducing the training cost. The key idea is to utilize a Mapping Network that maps a coarse field to a fine field to generate fine-scale training data. Compared to surrogate models which map parameters/structures to fine fields, Mapping Network is much easier to be trained and thus requires much less fine-scale data. In addition, it has much better transferability and can be easily adopted to a related but different task. Combined with transfer learning, the proposed scheme results in greatly reduced training costs compared to the approach without using Mapping Network. [ABSTRACT FROM AUTHOR]

Recently, more attention has been focused on the surrogate model using deep learning methods due to its powerful representational ability. However, it is usually challenging to obtain sufficient labeled samples for effective training because of the time-consuming numerical calculation, especially for the temperature field prediction of heat source layout (HSL-TFP). This work develops a novel and effective training method to overcome this problem for the deep surrogate model in HSL-TFP. First, the prediction of temperature field is modeled as an image-to-image regression problem, and the feature pyramid network (FPN) is chosen as the backbone of the deep network. Then, considering the inter-sample difference and the limited number of training samples, pairwise temperature field difference is utilized as data augmentation to train the surrogate model. Finally, deep transfer learning is introduced to take advantage of the valuable information from similar tasks and accelerate learning among different HSL-TFP problems. Experiments employing physic simulation data are conducted to validate the effectiveness of the proposed method. The results demonstrate that the proposed methods have significantly improved the prediction precision of the deep surrogate model with a small sample. [ABSTRACT FROM AUTHOR]

Engineering design research integrating artificial intelligence (AI) into computer-aided design (CAD) and computer-aided engineering (CAE) is actively being conducted. This study proposes a deep learning-based CAD/CAE framework in the conceptual design phase that automatically generates 3D CAD designs and evaluates their engineering performance. The proposed framework comprises seven stages: (1) 2D generative design, (2) dimensionality reduction, (3) design of experiment in latent space, (4) CAD automation, (5) CAE automation, (6) transfer learning, and (7) visualization and analysis. The proposed framework is demonstrated through a road wheel design case study and indicates that AI can be practically incorporated into an end-use product design project. Engineers and industrial designers can jointly review a large number of generated 3D CAD models by using this framework along with the engineering performance results estimated by AI and find conceptual design candidates for the subsequent detailed design stage. [ABSTRACT FROM AUTHOR]

A vital necessity when employing state-of-the-art deep neural networks (DNNs) for topology optimization is to predict near-optimal structures while satisfying pre-defined optimization constraints and objective function. Existing studies, on the other hand, suffer from the structural disconnections which result in unexpected errors in the objective and constraints. In this study, a two-stage network model is proposed using convolutional encoder-decoder networks that incorporate a new way of loss functions to reduce the number of structural disconnection cases as well as to reduce pixel-wise error to enhance the predictive performance of DNNs for topology optimization without any iteration. In the first stage, a single DNN model architecture is proposed and used in two parallel networks using two different loss functions for each called the mean square error (MSE) and mean absolute error (MAE). Once the priori information is generated from the first stage, it is instantly fed into the second stage, which acts as a rectifier network over the priori predictions. Finally, the second stage is trained using the binary cross-entropy (BCE) loss to provide the final predictions. The proposed two-stage network with the proposed loss functions is implemented for both two-dimensional (2D) and three-dimensional (3D) topology optimization datasets to observe its generalization ability. The validation results showed that the proposed two-stage framework could improve network prediction ability compared to a single network while significantly reducing compliance and volume fraction errors. [ABSTRACT FROM AUTHOR]

Topology optimization (TO) is a common technique used in free-form designs. However, conventional TO-based design approaches suffer from high computational cost due to the need for repetitive forward calculations and/or sensitivity analysis, which are typically done using high-dimensional simulations such as finite element analysis (FEA). In this work, artificial neural networks are used as efficient surrogate models for forward and sensitivity calculations in order to greatly accelerate the design process of topology optimization. To improve the accuracy of sensitivity analyses, dual-model artificial neural networks that are trained with both forward and sensitivity data are constructed and are integrated into the Solid Isotropic Material with Penalization (SIMP) method to replace the FEA. The performance of the accelerated SIMP method is demonstrated on two benchmark design problems namely minimum compliance design and metamaterial design. The efficiency gained in the problem with size of 64 × 64 is 137 times in forward calculation and 74 times in sensitivity analysis. In addition, effective data generation methods suitable for TO designs are investigated and developed, which lead to a great saving in training time. In both benchmark design problems, a design accuracy of 95% can be achieved with only around 2000 training data. [ABSTRACT FROM AUTHOR]

This study is focused on enhancing the computational efficiency of the solid isotropic material with penalization (SIMP) approach implemented for solving topology optimization problems. Solving such problems might become extremely time-consuming; in this direction, machine learning (ML) and specifically deep neural computing are integrated in order to accelerate the optimization procedure. The capability of ML-based computational models to extract multiple levels of representation of non-linear input data has been implemented successfully in various problems ranging from time series prediction to pattern recognition. The later one triggered the development of the methodology proposed in the current study that is based on deep belief networks (DBNs). More specifically, a DBN is calibrated on transforming the input data to a new higher-level representation. Input data contains the density fluctuation pattern of the finite element discretization provided by the initial steps of SIMP approach, and output data corresponds to the resulted density values distribution over the domain as obtained by SIMP. The representation capabilities and the computational advantages offered by the proposed DBN-based methodology coupled with the SIMP approach are investigated in several benchmark topology optimization test examples where it is observed more than one order of magnitude reduction on the iterations that were originally required by SIMP, while the advantages become more pronounced in case of large-scale problems. [ABSTRACT FROM AUTHOR]

Estimating unknown parameters or conditions based on observation in a numerical model is a problem considered in data assimilation. In this study, we investigate a data assimilation approach using an image-processing deep neural network (DNN) as a likelihood function. The DNN is trained by observed images and tests visualized images generated by numerical simulation. This approach does not provide exact comparison of observed and simulated images for constructing the likelihood function. However, it would be effective when exact comparison is difficult due to noise or complex measurement procedures. The effectiveness of this approach is investigated by a vortex flow around a circular cylinder moving freely in the crossflow direction, realizing vortex-induced vibration (VIV). The DNN trained by wake visualization images from the VIV experiment tests pseudo-wake images from the numerical simulation to estimate VIV amplitude and frequency parameters. By evaluating the confidence score of the DNN from the simulated images with different amplitude and frequency values, these input parameters can be estimated based on the experimental VIV images, resulting in data assimilation with a likelihood function based on the DNN. The results showed that the amplitude and frequency of the VIV can be approximated from the experimental images. [ABSTRACT FROM AUTHOR]

Due to their designable properties, microstructural materials have emerged as an important class of materials that have the potential for used in a variety of applications. The design of such materials is challenged by the multifunctionality requirements and various constraints stemmed from manufacturing limitations and other practical considerations. Traditional design methods such as those based on topological optimization techniques rely heavily on high-dimensional physical simulations and can be inefficient. In addition, it is difficult to impose geometrical constraints in those methods. In this work, we propose a deep learning model based on deep convolutional generative adversarial network (DCGAN) and convolutional neural network (CNN) for the design of microstructural materials. The DCGAN is used to generate design candidates that satisfy geometrical constraints and the CNN is used as a surrogate model to link the microstructure to its properties. Once trained, the two networks are combined to form the design network which is utilized to for the inverse design. The advantages of the method include its high efficiency and the simplicity in handling geometrical constraints. In addition, no high-dimensional sensitivity simulations are required. The performance of the method is demonstrated on the design of microstructural materials with desired compliance tensor, subject to specified geometrical constraints. [ABSTRACT FROM AUTHOR]

In this study, we propose a novel deep learning-based method to predict an optimized structure for a given boundary condition and optimization setting without using any iterative scheme. For this purpose, first, using open-source topology optimization code, datasets of the optimized structures paired with the corresponding information on boundary conditions and optimization settings are generated at low (32 × 32) and high (128 × 128) resolutions. To construct the artificial neural network for the proposed method, a convolutional neural network (CNN)-based encoder and decoder network is trained using the training dataset generated at low resolution. Then, as a two-stage refinement, the conditional generative adversarial network (cGAN) is trained with the optimized structures paired at both low and high resolutions and is connected to the trained CNN-based encoder and decoder network. The performance evaluation results of the integrated network demonstrate that the proposed method can determine a near-optimal structure in terms of pixel values and compliance with negligible computational time. [ABSTRACT FROM AUTHOR]