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PyTOaCNN: Topology optimization using an adaptive convolutional neural network in Python
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DOI：10.1007/s00500-025-10919-y.png)
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Abstract
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This paper introduces an adaptive convolutional neural network (CNN) architecture capable of automating various topology optimization (TO) problems with diverse underlying physics. The proposed architecture has an encoder-decoder-type structure with dense layers added at the bottleneck region to capture geometrical features. To further improve the network’s ability to capture intricate geometry, an adaptive layer with user-defined neurons is incorporated into the dense layers. TensorFlow and Keras are the main libraries employed to develop and train the model. The network is trained using datasets obtained by the problem-specific open-source TO codes. The model takes the user’s input of the volume fraction as an image and instantly generates an optimized design post-training. To demonstrate the effectiveness and robustness of the proposed adaptive CNN model various numerical experiments that include compliance minimization problems with constant and design-dependent loads and bulk modulus optimization are performed. The model produces high-quality results for test problems resembling those obtained by open-source TO codes with insignificant objective and volume fraction errors. To facilitate reproducibility and ease of learning for those new to the field, the paper also includes the associated Python code (Appendix A) and explains it.
Keywords:
Topology Optimization
Machine Learning
Python Code
Convolutional Neural Network
Design-Dependent Loads
Bulk Modulus Optimization
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