Abstract
Electromagnetic fields are commonly controlled through geometric design, but existing approaches often lack efficient and differentiable modeling tools for complex shapes. Here we introduce Electromagnetic Sculptor, a differentiable geometric optimization framework for manipulating electromagnetic fields on arbitrarily meshed structures. The framework combines a numerical electromagnetic model based on shooting and bouncing rays with a gradient-based geometric optimizer that stabilizes mesh deformation through spatial filtering. To avoid excessive shape distortion during optimization, a shape-preserving regularization strategy is incorporated. The method is demonstrated using radar cross section reduction as a representative application. Numerical and experimental results show pronounced field suppression at both single frequencies and across a broadband range, while maintaining geometric smoothness and manufacturability. The framework enables fast optimization for models containing thousands of vertices, with simulated results consistent with experimental measurements. These results illustrate how differentiable computation can be integrated with physically grounded electromagnetic modeling and practical design constraints.
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Data availability
The RCS measurement data used in this research have been uploaded to the Supplementary Data. Additionally, the RCS measurement data and mesh files used can be accessed via https://github.com/yankaiqiao/EM-Sculptor/.
Code availability
The code used in this study is available from the corresponding authors upon reasonable request.
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Acknowledgements
This work was supported by the National Key Research and Development Program of China under Grant No. 2023YFB3811501, National Natural Science Foundation of China under Grant Nos. 62301146 and 62288101, Natural Science Foundation of Jiangsu Province of China under Grant No. BK20230816, China Postdoctoral Science Foundation under Grant Nos. 2023M730554 and BX20220065 and Postgraduate Research and Practice Innovation Program of Jiangsu Province under Grant No. KYCX25_0463.
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Kaiqiao Yang and Che Liu contributed equally to this work. Tie Jun Cui and Wenming Yu supervised the research. All authors contributed to the data analysis and revision of the manuscript.
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Communications Engineering thanks the anonymous reviewers for their contribution to the peer review of this work. Primary Handling Editors: [Yu-Cheng Chen] and [Wenjie Wang]. A peer review file is available.
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Yang, K., Liu, C., Yu, W. et al. Electromagnetic Sculptor: a differentiable geometric optimization framework to manipulate electromagnetic fields. Commun Eng (2026). https://doi.org/10.1038/s44172-026-00642-3
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DOI: https://doi.org/10.1038/s44172-026-00642-3
