volume | PIER Journals

Abstract

Long-range near-field magnetic resonance wireless power transfer (WPT) technology holds broad application prospects in fields such as medical implants and industrial manufacturing robots. However, it faces challenges of low efficiency and poor robustness in long-distance transmission. This study proposes an innovative collaborative optimization approach that integrates the machine learning gradient descent optimization algorithm (GDOA) with non-Hermitian topological physics to precisely regulate the coupling strength distribution, thereby realizing a highly flexible, efficient, and robust WPT system capable of anchoring transmission frequencies and accommodating an arbitrary number of resonators. Experimental results demonstrate that the GDOA-optimized Su-Schrieffer-Heeger (SSH)-like topological chain achieves a transmission efficiency of 65% at the target frequency and maintains 57.9% efficiency under 30% structural perturbations, significantly outperforming the SSH chain (45.6%) and uniform chain (24.1%) in control groups. This research provides theoretical and experimental support for the design of machine learning-based topological long-range WPT systems, offering substantial practical value, particularly in medical electronic power supply and wireless industrial equipment applications.

1. Tesla, Nikola, "Apparatus for transmitting electrical energy," U.S. Patent, US1119732A, 1914.
doi:10.1038/scientificamerican06041904-23760supp

2. Kurs, A., Aristeidis Karalis, Robert Moffatt, J. D. Joannopoulos, Peter Fisher, and Marin Soljačić, "Wireless power transfer via strongly coupled magnetic resonances," Science, Vol. 317, No. 5834, 83-86, 2007.
doi:10.1126/science.1143254

3. Ahn, Dukju and Songcheol Hong, "Wireless power transmission with self-regulated output voltage for biomedical implant," IEEE Transactions on Industrial Electronics, Vol. 61, No. 5, 2225-2235, 2013.
doi:10.1109/tie.2013.2273472

4. Kim, Sanghoek, John S. Ho, and Ada S. Y. Poon, "Midfield wireless powering of subwavelength autonomous devices," Physical Review Letters, Vol. 110, No. 20, 203905, 2013.
doi:10.1103/physrevlett.110.203905

5. Ho, John S., Alexander J. Yeh, Evgenios Neofytou, Sanghoek Kim, Yuji Tanabe, Bhagat Patlolla, Ramin E. Beygui, and Ada S. Y. Poon, "Wireless power transfer to deep-tissue microimplants," Proceedings of the National Academy of Sciences, Vol. 111, No. 22, 7974-7979, 2014.
doi:10.1073/pnas.1403002111

6. Mei, Henry and Pedro P. Irazoqui, "Miniaturizing wireless implants," Nature Biotechnology, Vol. 32, No. 10, 1008-1010, 2014.
doi:10.1038/nbt.3038

7. Lu, Xiao, Dusit Niyato, Ping Wang, Dong In Kim, and Zhu Han, "Wireless charger networking for mobile devices: Fundamentals, standards, and applications," IEEE Wireless Communications, Vol. 22, No. 2, 126-135, 2015.
doi:10.1109/mwc.2015.7096295

8. Lerosey, Geoffroy, "Wireless power on the move," Nature, Vol. 546, No. 7658, 354-355, 2017.
doi:10.1038/546354a

9. Sample, Alanson P., David T. Meyer, and Joshua R. Smith, "Analysis, experimental results, and range adaptation of magnetically coupled resonators for wireless power transfer," IEEE Transactions on Industrial Electronics, Vol. 58, No. 2, 544-554, 2010.
doi:10.1109/tie.2010.2046002

10. Miao, Zhidong, Dake Liu, and Chen Gong, "Efficiency enhancement for an inductive wireless power transfer system by optimizing the impedance matching networks," IEEE Transactions on Biomedical Circuits and Systems, Vol. 11, No. 5, 1160-1170, 2017.
doi:10.1109/tbcas.2017.2740266

11. Li, Hongchang, Jie Li, Kangping Wang, Wenjie Chen, and Xu Yang, "A maximum efficiency point tracking control scheme for wireless power transfer systems using magnetic resonant coupling," IEEE Transactions on Power Electronics, Vol. 30, No. 7, 3998-4008, 2014.
doi:10.1109/tpel.2014.2349534

12. Guo, Zhiwei, Fengqing Yang, Haiyan Zhang, Xian Wu, Qiong Wu, Kejia Zhu, Jun Jiang, Haitao Jiang, Yaping Yang, Yunhui Li, and Hong Chen, "Level pinning of anti-PT-symmetric circuits for efficient wireless power transfer," National Science Review, Vol. 11, No. 1, nwad172, 2024.
doi:10.1093/nsr/nwad172

13. Zhong, Wenxing, Chi Kwan Lee, and S. Y. Ron Hui, "General analysis on the use of Tesla's resonators in domino forms for wireless power transfer," IEEE Transactions on Industrial Electronics, Vol. 60, No. 1, 261-270, 2011.
doi:10.1109/tie.2011.2171176

14. Kim, Jin Wook, Hyeon-Chang Son, Kwan-Ho Kim, and Young-Jin Park, "Efficiency analysis of magnetic resonance wireless power transfer with intermediate resonant coil," IEEE Antennas and Wireless Propagation Letters, Vol. 10, 389-392, 2011.
doi:10.1109/lawp.2011.2150192

15. Saha, Chitta, Ihechiluru Anya, Cristina Alexandru, and Robert Jinks, "Wireless power transfer using relay resonators," Applied Physics Letters, Vol. 112, No. 26, 263902, 2018.
doi:10.1063/1.5022032

16. Sakhdari, Maryam, Mehdi Hajizadegan, and Pai-Yen Chen, "Robust extended-range wireless power transfer using a higher-order PT-symmetric platform," Physical Review Research, Vol. 2, No. 1, 013152, 2020.
doi:10.1103/physrevresearch.2.013152

17. Guo, Zhiwei, Jie Jiang, Xian Wu, Haiyan Zhang, Shengyu Hu, Yuqian Wang, Yunhui Li, Yaping Yang, and Hong Chen, "Rotation manipulation of high-order PT-symmetry for robust wireless power transfer," Fundamental Research, Vol. 11, 10, 2023.
doi:10.1016/j.fmre.2023.11.010

18. Song, Mingzhao, Prasad Jayathurathnage, Esmaeel Zanganeh, Mariia Krasikova, Pavel Smirnov, Pavel Belov, Polina Kapitanova, Constantin Simovski, Sergei Tretyakov, and Alex Krasnok, "Wireless power transfer based on novel physical concepts," Nature Electronics, Vol. 4, No. 10, 707-716, 2021.
doi:10.1038/s41928-021-00658-x

19. Zeng, Chao, Zhiwei Guo, Kejia Zhu, Caifu Fan, Guo Li, Jun Jiang, Yunhui Li, Haitao Jiang, Yaping Yang, Yong Sun, and Hong Chen, "Efficient and stable wireless power transfer based on the non-Hermitian physics," Chinese Physics B, Vol. 31, No. 1, 010307, 2022.
doi:10.1088/1674-1056/ac3815

20. Assawaworrarit, Sid, Xiaofang Yu, and Shanhui Fan, "Robust wireless power transfer using a nonlinear parity-time-symmetric circuit," Nature, Vol. 546, No. 7658, 387-390, 2017.
doi:10.1038/nature22404

21. Zhou, Jiali, Bo Zhang, Wenxun Xiao, Dongyuan Qiu, and Yanfeng Chen, "Nonlinear parity-time-symmetric model for constant efficiency wireless power transfer: Application to a drone-in-flight wireless charging platform," IEEE Transactions on Industrial Electronics, Vol. 66, No. 5, 4097-4107, 2018.
doi:10.1109/tie.2018.2864515

22. Feis, J., C. J. Stevens, and E. Shamonina, "Wireless power transfer through asymmetric topological edge states in diatomic chains of coupled meta-atoms," Applied Physics Letters, Vol. 117, No. 13, 134106, 2020.
doi:10.1063/5.0024077

23. Song, Juan, Fengqing Yang, Zhiwei Guo, Xian Wu, Kejia Zhu, Jun Jiang, Yong Sun, Yunhui Li, Haitao Jiang, and Hong Chen, "Wireless power transfer via topological modes in dimer chains," Physical Review Applied, Vol. 15, No. 1, 014009, 2021.
doi:10.1103/physrevapplied.15.014009

24. Zhang, Li, Yihao Yang, Zhao Jiang, Qiaolu Chen, Qinghui Yan, Zhouyi Wu, Baile Zhang, Jiangtao Huangfu, and Hongsheng Chen, "Demonstration of topological wireless power transfer," Science Bulletin, Vol. 66, No. 10, 974-980, 2021.
doi:10.1016/j.scib.2021.01.028

25. Yang, Fengqing, Juan Song, Zhiwei Guo, Xian Wu, Kejia Zhu, Jun Jiang, Yong Sun, Haitao Jiang, Yunhui Li, and Hong Chen, "Actively controlled asymmetric edge states for directional wireless power transfer," Optics Express, Vol. 29, No. 5, 7844-7857, 2021.
doi:10.1364/oe.417887

26. Zhang, Haiyan, Zhiwei Guo, Yunhui Li, Yaping Yang, Yuguang Chen, and Hong Chen, "A universal non-Hermitian platform for bound state in the continuum enhanced wireless power transfer," Frontiers of Physics, Vol. 19, No. 4, 43209, 2024.
doi:10.1007/s11467-023-1388-x

27. Ma, Wei, Zhaocheng Liu, Zhaxylyk A. Kudyshev, Alexandra Boltasseva, Wenshan Cai, and Yongmin Liu, "Deep learning for the design of photonic structures," Nature Photonics, Vol. 15, No. 2, 77-90, 2021.
doi:10.1038/s41566-020-0685-y

28. Genty, Goëry., Lauri Salmela, John M. Dudley, Daniel Brunner, Alexey Kokhanovskiy, Sergei Kobtsev, and Sergei K. Turitsyn, "Machine learning and applications in ultrafast photonics," Nature Photonics, Vol. 15, No. 2, 91-101, 2021.
doi:10.1038/s41566-020-00716-4

29. Nadell, Christian C., Bohao Huang, Jordan M. Malof, and Willie J. Padilla, "Deep learning for accelerated all-dielectric metasurface design," Optics Express, Vol. 27, No. 20, 27523-27535, 2019.
doi:10.1364/oe.27.027523

30. Wu, Yadong, Zengming Meng, Kai Wen, Chengdong Mi, Jing Zhang, and Hui Zhai, "Active learning approach to optimization of experimental control," Chinese Physics Letters, Vol. 37, No. 10, 103201, 2020.
doi:10.1088/0256-307x/37/10/103201

31. Henson, Bryce M., Dong K. Shin, Kieran F. Thomas, Jacob A. Ross, Michael R. Hush, Sean S. Hodgman, and Andrew G. Truscott, "Approaching the adiabatic timescale with machine learning," Proceedings of the National Academy of Sciences, Vol. 115, No. 52, 13216-13221, 2018.
doi:10.1073/pnas.1811501115

32. Nakamura, Ippei, Atsunori Kanemura, Takumi Nakaso, Ryuta Yamamoto, and Takeshi Fukuhara, "Non-standard trajectories found by machine learning for evaporative cooling of 87Rb atoms," Optics Express, Vol. 27, No. 15, 20435-20443, 2019.
doi:10.1364/oe.27.020435

33. Bukov, Marin, Alexandre G. R. Day, Dries Sels, Phillip Weinberg, Anatoli Polkovnikov, and Pankaj Mehta, "Reinforcement learning in different phases of quantum control," Physical Review X, Vol. 8, No. 3, 031086, 2018.
doi:10.1103/physrevx.8.031086

34. Guo, Shuai-Feng, Feng Chen, Qi Liu, Ming Xue, Jun-Jie Chen, Jia-Hao Cao, Tian-Wei Mao, Meng Khoon Tey, and Li You, "Faster state preparation across quantum phase transition assisted by reinforcement learning," Physical Review Letters, Vol. 126, No. 6, 060401, 2021.
doi:10.1103/physrevlett.126.060401

35. Lin, Jian, Zhong Yuan Lai, and Xiaopeng Li, "Quantum adiabatic algorithm design using reinforcement learning," Physical Review A, Vol. 101, No. 5, 052327, 2020.
doi:10.1103/physreva.101.052327

36. Schiffer, Benjamin F., Jordi Tura, and J. Ignacio Cirac, "Adiabatic spectroscopy and a variational quantum adiabatic algorithm," PRX Quantum, Vol. 3, No. 2, 020347, 2022.
doi:10.1103/prxquantum.3.020347

37. Mukherjee, Rick, Harry Xie, and Florian Mintert, "Bayesian optimal control of Greenberger-Horne-Zeilinger states in Rydberg lattices," Physical Review Letters, Vol. 125, No. 20, 203603, 2020.
doi:10.1103/physrevlett.125.203603

38. Choi, Byeong-Guk and Yun-Su Kim, "New structure design of ferrite cores for wireless electric vehicle charging by machine learning," IEEE Transactions on Industrial Electronics, Vol. 68, No. 12, 12162-12172, 2021.
doi:10.1109/tie.2020.3047041

39. Rahulkumar, J. and R. Narayanamoorthi, "Delta and inverse delta coupler optimization using machine learning for wireless power transfer electric vehicle charging application," IEEE Transactions on Power Electronics, Vol. 40, No. 1, 2556-2568, 2025.
doi:10.1109/tpel.2024.3462980

40. Liu, Xu, Jie Chao, Cancan Rong, Zhijuan Liao, and Chenyang Xia, "Compatibility and performance improvement of the WPT systems based on Q-learning algorithm," IEEE Transactions on Power Electronics, Vol. 39, No. 8, 10582-10593, 2024.
doi:10.1109/tpel.2024.3397804

41. Srivastava, Vivek Kumar, Arhum Ahmad, and Ashwani Sharma, "A machine learning assisted localization and magnetic field forming for wireless powering of biomedical implant devices," IEEE Transactions on Antennas and Propagation, Vol. 72, No. 11, 8590-8599, 2024.
doi:10.1109/tap.2024.3459617

42. Magann, Alicia B., Kenneth M. Rudinger, Matthew D. Grace, and Mohan Sarovar, "Feedback-based quantum optimization," Physical Review Letters, Vol. 129, No. 25, 250502, 2022.

43. See Supplemental Material at *** for detailed derivations of GDOA validation, the imaginary parts of the eigenfrequencies in SSH, and more experimental results.

44. Fan, Shanhui, Wonjoo Suh, and J. D. Joannopoulos, "Temporal coupled-mode theory for the Fano resonance in optical resonators," Journal of the Optical Society of America A, Vol. 20, No. 3, 569-572, 2003.
doi:10.1364/JOSAA.20.000569

45. Guo, Zhiwei, Tengzhou Zhang, Juan Song, Haitao Jiang, and Hong Chen, "Sensitivity of topological edge states in a non-Hermitian dimer chain," Photonics Research, Vol. 9, No. 4, 574-582, 2021.
doi:10.1364/prj.413873

46. Song, Wange, Wenzhao Sun, Chen Chen, Qinghai Song, Shumin Xiao, Shining Zhu, and Tao Li, "Breakup and recovery of topological zero modes in finite non-Hermitian optical lattices," Physical Review Letters, Vol. 123, No. 16, 165701, 2019.
doi:10.1103/physrevlett.123.165701

47. Shiba, Kenji, Akira Morimasa, and Harutoyo Hirano, "Design and development of low-loss transformer for powering small implantable medical devices," IEEE Transactions on Biomedical Circuits and Systems, Vol. 4, No. 2, 77-85, 2010.
doi:10.1109/tbcas.2009.2034364

48. Beh, Teck Chuan, Masaki Kato, Takehiro Imura, Sehoon Oh, and Yoichi Hori, "Automated impedance matching system for robust wireless power transfer via magnetic resonance coupling," IEEE Transactions on Industrial Electronics, Vol. 60, No. 9, 3689-3698, 2012.
doi:10.1109/tie.2012.2206337

49. Long, Yang, Jie Ren, and Hong Chen, "Unsupervised manifold clustering of topological phononics," Physical Review Letters, Vol. 124, No. 18, 185501, 2020.
doi:10.1103/physrevlett.124.185501

50. Long, Yang and Baile Zhang, "Unsupervised data-driven classification of topological gapped systems with symmetries," Physical Review Letters, Vol. 130, No. 3, 036601, 2023.
doi:10.1103/physrevlett.130.036601

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Prof. Yunhui Li

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Dr. Zhiwei Guo