An Adaptive and Scalable ANN-based Model-Order-Reduction Method for Large-Scale TO Designs

Topology Optimization (TO) provides a systematic approach for obtaining structure design with optimum performance of interest. However, the process requires numerical evaluation of objective function and constraints at each iteration, which is computational expensive especially for large-scale design. 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 are generated mostly through simulations. The data generation time scales rapidly with the design domain size, decreasing the efficiency of the method itself. Another major issue is the weak generalizability of most 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 a 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. Moreover, by using domain fragmentation, the transferability of the MapNet is largely improved. Specifically, 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.

An adaptive artificial neural network-based generative design method for layout designs

Layout designs are encountered in a variety of fields. For problems with many design degrees of freedom, efficiency of design methods becomes a major concern. In recent years, machine learning methods such as artificial neural networks have been used increasingly to speed up the design process. A main issue of many such approaches is the need for a large corpus of training data that are generated using high-dimensional simulations. The high computational cost associated with training data generation largely diminishes the efficiency gained by using machine learning methods. In this work, an adaptive artificial neural network-based generative design approach is proposed and developed. This method uses a generative adversarial network to generate design candidates and thus the number of design variables is greatly reduced. To speed up the evaluation of the objective function, a convolutional neural network is constructed as the surrogate model for function evaluation. The inverse design is carried out using the genetic algorithm in conjunction with two neural networks. A novel adaptive learning and optimization strategy is proposed, which allows the design space to be effectively explored for the search for optimal solutions. As such the number of training data needed is greatly reduced. The performance of the proposed design method is demonstrated on two heat source layout design problems. In both problems, optimal designs have been obtained. Compared with several existing approaches, the proposed approach has the best performance in terms of accuracy and efficiency.

Accelerating gradient-based topology optimization design with dual-model neural networks

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, 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 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 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 64x64 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.

Deep learning based inverse method for layout design

Layout design with complex constraints is a challenging problem 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.