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Authors
Deng, Hao
Paulson, Noah
Messner, Mark C.
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Article History
Received: 22 May 2025
Revised: 24 November 2025
Accepted: 10 December 2025
First Online: 2 January 2026
Declarations
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: On behalf of all authors, the corresponding author states that there is no conflict of interest.
: The numerical examples and training procedures described in this work are based on customized Python implementations. All relevant data, model architecture details, and optimization settings are provided in the manuscript. The authors are willing to share the Python code used for the autoencoder training and BADS-based optimization upon reasonable request. Due to licensing restrictions, the finite element solver (used for density field evaluation and homogenization) cannot be made publicly available. However, instructions for implementing similar procedures using open-source alternatives such as MOOSE or FEniCS are discussed in the manuscript.
