journal article·2026-02Open access

Physics‐Informed Deep Learning Method for Real‐Time Multi‐Harmonic Beamforming Based on Space‐Time‐Coding Metasurface

Jiang Han Bao, Che Liu, Yi Ning Zheng, Lei Zhang, Wen Ming Yu, Lianlin Li, Tie Jun Cui

Advanced Electronic Materials· Volume 12· Issue 3

Abstract

ABSTRACT Space‐time‐coding metasurfaces (STCMs) enable simultaneous controls of electromagnetic wave across multiple harmonics, but designing high‐performance coding sequences in real time remains challenging. Here, we propose an unsupervised physics‐informed deep learning framework that can generate optimal spatiotemporal coding patterns for arbitrary single‐ and dual‐beam requirements at each harmonic frequency. The proposed method features three key innovations: physics‐informed mechanisms to enable unsupervised learning without requiring paired training data, a dedicated strategy for multi‐bit metasurface configurations, and the Conflict Averse Gradient descent (CAGrad) method to coordinate the parameter optimization across harmonics in multi‐task learning. Experiments on a 2‐bit STCM demonstrate robust beamforming capabilities over five harmonics, achieving an average radiation difference of 1.55 dB and real‐time design <0.1s. This is a 4‐order‐of‐magnitude improvement in computational efficiency compared with the particle swarm optimization methods. This work establishes a real‐time and physics‐aware design paradigm for intelligent metasurfaces in the next‐generation wireless systems.
Source: crossref · Quality: baseline

Research context

OpenAlex topics: Advanced Wireless Communication Technologies · Metamaterials and Metasurfaces Applications · Energy Harvesting in Wireless Networks

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

State Key Laboratory of Millimeter Wave Southeast University Nanjing China

Institute of Electromagnetic Space Southeast University Nanjing China

State Key Laboratory of Advanced Optical Communication Systems and Networks Peking University Beijing China

Funding

National Natural Science Foundation of China · Natural Science Foundation of Jiangsu Province · China Postdoctoral Science Foundation

References (40)

Show source-provided references
1. 10.1038/nmat343110.1038/nmat3431 ↗
2. 10.1126/science.112590710.1126/science.1125907 ↗
3. 10.1126/science.121071310.1126/science.1210713 ↗
4. 10.1103/PhysRevLett.85.396610.1103/PhysRevLett.85.3966 ↗
5. 10.1126/science.113362810.1126/science.1133628 ↗
6. 10.1103/PhysRevLett.101.20390110.1103/PhysRevLett.101.203901 ↗
7. 10.1126/science.116694910.1126/science.1166949 ↗
8. 10.1103/PhysRevLett.111.17390110.1103/PhysRevLett.111.173901 ↗
9. 10.1103/PhysRevLett.102.25390210.1103/PhysRevLett.102.253902 ↗
10. 10.1364/PRJ.41205210.1364/PRJ.412052 ↗
11. Cui T. J. · 2009
12. 10.1007/978-981-99-7914-110.1007/978-981-99-7914-1 ↗
13. 10.3389/fphy.2020.59341110.3389/fphy.2020.593411 ↗
14. 10.1038/lsa.2014.9910.1038/lsa.2014.99 ↗
15. 10.1038/s41467-018-06802-010.1038/s41467-018-06802-0 ↗
16. 10.34133/2021/980267310.34133/2021/9802673 ↗
17. 10.1038/s41467-025-61934-410.1038/s41467-025-61934-4 ↗
18. 10.1109/JSAC.2024.338912410.1109/JSAC.2024.3389124 ↗
19. 10.1002/adfm.20200762010.1002/adfm.202007620 ↗
20. J.KennedyandR.Eberhart “Particle Swarm Optimization ”Proceedings of ICNN′95 – International Conference on Neural Networks 4 IEEE New York:1995 pp.1942–1948.10.1109/ICNN.1995.488968 ↗
21. 10.1002/advs.20190012810.1002/advs.201900128 ↗
22. 10.1109/JETCAS.2020.297276410.1109/JETCAS.2020.2972764 ↗
23. 10.1109/OJAP.2023.329210810.1109/OJAP.2023.3292108 ↗
24. 10.1364/AO.48786710.1364/AO.487867 ↗
25. 10.1117/1.APN.2.1.01601010.1117/1.APN.2.1.016010 ↗
26. 10.1002/adpr.20220011010.1002/adpr.202200110 ↗
27. 10.1364/PRJ.41628710.1364/PRJ.416287 ↗
28. 10.1016/j.isci.2024.11059510.1016/j.isci.2024.110595 ↗
29. 10.1063/5.013263510.1063/5.0132635 ↗
30. 10.1002/adfm.20240357710.1002/adfm.202403577 ↗
31. 10.1038/nature1453910.1038/nature14539 ↗
32. 10.1002/advs.20240455810.1002/advs.202404558 ↗
33. 2018 · 79
34. K.He X.Zhang S.Ren andJ.Sun “Deep Residual Learning for Image Recognition ”2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) IEEE New York2015 770–778.10.1109/CVPR.2016.90 ↗
35. 10.1109/TKDE.2021.307020310.1109/TKDE.2021.3070203 ↗
36. B.Liu X.Liu X.Jin P.Stone andQ.Liu “Conflict‐Averse Gradient Descent for Multi‐task Learning ” inProceedings of the 35th International Conference on Neural Information Processing Systems NIPS′21 Curran Associates Inc Red Hook NY USA2021.
37. A.Paszke S.Gross F.Massa et al.PyTorch: an Imperative Style High‐performance Deep Learning Library in Proceedings of the 33rd International Conference on Neural Information Processing Systems (NIPS) Curran Associates Inc Vancouver Canada(2019):8026–8037.
38. D.KingmaandJ.Ba “Adam: a Method for Stochastic Optimization ” InInternational Conference on Learning Representations (ICLR) San Diega CA USA2015.
39. D.Ulyanow A.Vedaldi andL. V.Lempitsky Instance Normalization: the Missing Ingredient for Fast Stylization CoRR2016 https://arxiv.org/abs/1607.08022.
40. A. F.Agarap Deep Learning using Rectified Linear Units (ReLU) CoRR2018 https://arxiv.org/abs/1803.08375.