Abstract
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.
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An open-source 2D topology optimization MATLAB code (Andreassen et al. 2011) and 3D topology optimization code (Liu and Tovar 2014) were used to generate data. All codes for neural networks were written in Python 3.7. For neural networks, Keras (Chollet François 2015) with Tensorflow backend (Abadi et al. 2016) was used.
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All necessary information to obtain the topology optimization data and the neural network models which allow to reproduce the results was provided in this paper. The results described in this paper can be replicated by implementing this information. The numerical codes to reproduce the results can also be provided by the corresponding author with a reasonable request.
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Ates, G.C., Gorguluarslan, R.M. Two-stage convolutional encoder-decoder network to improve the performance and reliability of deep learning models for topology optimization. Struct Multidisc Optim 63, 1927–1950 (2021). https://doi.org/10.1007/s00158-020-02788-w
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DOI: https://doi.org/10.1007/s00158-020-02788-w