Vol. 122
Latest Volume
All Volumes
PIERM 127 [2024] PIERM 126 [2024] PIERM 125 [2024] PIERM 124 [2024] PIERM 123 [2024] PIERM 122 [2023] PIERM 121 [2023] PIERM 120 [2023] PIERM 119 [2023] PIERM 118 [2023] PIERM 117 [2023] PIERM 116 [2023] PIERM 115 [2023] PIERM 114 [2022] PIERM 113 [2022] PIERM 112 [2022] PIERM 111 [2022] PIERM 110 [2022] PIERM 109 [2022] PIERM 108 [2022] PIERM 107 [2022] PIERM 106 [2021] PIERM 105 [2021] PIERM 104 [2021] PIERM 103 [2021] PIERM 102 [2021] PIERM 101 [2021] PIERM 100 [2021] PIERM 99 [2021] PIERM 98 [2020] PIERM 97 [2020] PIERM 96 [2020] PIERM 95 [2020] PIERM 94 [2020] PIERM 93 [2020] PIERM 92 [2020] PIERM 91 [2020] PIERM 90 [2020] PIERM 89 [2020] PIERM 88 [2020] PIERM 87 [2019] PIERM 86 [2019] PIERM 85 [2019] PIERM 84 [2019] PIERM 83 [2019] PIERM 82 [2019] PIERM 81 [2019] PIERM 80 [2019] PIERM 79 [2019] PIERM 78 [2019] PIERM 77 [2019] PIERM 76 [2018] PIERM 75 [2018] PIERM 74 [2018] PIERM 73 [2018] PIERM 72 [2018] PIERM 71 [2018] PIERM 70 [2018] PIERM 69 [2018] PIERM 68 [2018] PIERM 67 [2018] PIERM 66 [2018] PIERM 65 [2018] PIERM 64 [2018] PIERM 63 [2018] PIERM 62 [2017] PIERM 61 [2017] PIERM 60 [2017] PIERM 59 [2017] PIERM 58 [2017] PIERM 57 [2017] PIERM 56 [2017] PIERM 55 [2017] PIERM 54 [2017] PIERM 53 [2017] PIERM 52 [2016] PIERM 51 [2016] PIERM 50 [2016] PIERM 49 [2016] PIERM 48 [2016] PIERM 47 [2016] PIERM 46 [2016] PIERM 45 [2016] PIERM 44 [2015] PIERM 43 [2015] PIERM 42 [2015] PIERM 41 [2015] PIERM 40 [2014] PIERM 39 [2014] PIERM 38 [2014] PIERM 37 [2014] PIERM 36 [2014] PIERM 35 [2014] PIERM 34 [2014] PIERM 33 [2013] PIERM 32 [2013] PIERM 31 [2013] PIERM 30 [2013] PIERM 29 [2013] PIERM 28 [2013] PIERM 27 [2012] PIERM 26 [2012] PIERM 25 [2012] PIERM 24 [2012] PIERM 23 [2012] PIERM 22 [2012] PIERM 21 [2011] PIERM 20 [2011] PIERM 19 [2011] PIERM 18 [2011] PIERM 17 [2011] PIERM 16 [2011] PIERM 14 [2010] PIERM 13 [2010] PIERM 12 [2010] PIERM 11 [2010] PIERM 10 [2009] PIERM 9 [2009] PIERM 8 [2009] PIERM 7 [2009] PIERM 6 [2009] PIERM 5 [2008] PIERM 4 [2008] PIERM 3 [2008] PIERM 2 [2008] PIERM 1 [2008]
2023-12-12
Solving Electromagnetic Wave Scattering Using Artificial Neural Networks
By
Progress In Electromagnetics Research M, Vol. 122, 31-39, 2023
Abstract
Electromagnetic wave scattering (EMWS) is one of the complexities in electromagnetism. Traditionally, three numerical methods are used to solve this problem which are finite element method, finite difference method, and method of moments. Recently, artificial neural networks (ANNs) have gained popularity as tools to solve different problems in a wide variety of disciplines, including electromagnetism. This paper shows that the second ordinary differential equation that represents EMWS from one-dimensional, two-dimensional, and three-dimensional inhomogeneous mediums and deals with complex numbers can be solved using ANN. This is done by reducing the error between the trail solution at the output of the ANN and the second ordinary differential equation that represents the scattered field. The results from solving classical examples using the suggested approach are accurate.
Citation
Mohammad Ahmad, "Solving Electromagnetic Wave Scattering Using Artificial Neural Networks," Progress In Electromagnetics Research M, Vol. 122, 31-39, 2023.
doi:10.2528/PIERM23102603
References

1. Warnick, Karl F., Numerical Methods For Engineering An Introduction Using Matlab and Computational Electromagnetics Examples, 2 Ed., The Institution of Engineering and Technology, Croydon, UK, 2020.
doi:10.1049/SBEW548E

2. Jin, J., The Finite Element Method in Electromagnetics, 3 Ed., Wiley, IEEE Press, NY, USA, 2014.

3. Özgün, Ö. and M. Kuzuoğlu, Matlab-based Finite Element Programming in Electromagnetic Modeling, 1 Ed., CRC Press, Taylor & Francis Group, FL, USA, 2019.

4. Taflove, A. and S. C. Hagness, Computational Electrodynamics: The Finite-difference Time-domain Method, 3 Ed., Artech House, MA, USA, 2005.

5. Elsherbeni, A. and V. Demir, The Finite-Difference Time-Domain Method for Electromagnetics with MATLAB Simulations, 2 Ed., SciTech Publishing Inc., NJ, USA, 2016.

6. Harrington, Roger F., Field Computation by Moment Methods, Wiley-IEEE Press, NY, USA, 1993.
doi:10.1109/9780470544631

7. Gibson, Walton C., The Method of Moments in Electromagnetics, 3 Ed., CRC Press, NY, USA, 2021.
doi:10.1201/9780429355509

8. Olshanskii, Maxim A. and Eugene E. Tyrtyshnikov, Iterative Methods For Linear Systems: Theory and Applications, SIAM, PHL, USA, 2014.
doi:10.1137/1.9781611973464

9. Glassner, Andrew, Deep Learning: A Visual Approach, No Starch Press, CA, USA, 2021.

10. Krizhevsky, Alex, Ilya Sutskever, and Geoffrey E. Hinton, "Imagenet classification with deep convolutional neural networks," Proc. 25th Int. Conf. Neural Inf. Process. Syst., 1097–1105, 2013.
doi:10.1145/3065386

11. Ibtehaz, Nabil and M. Sohel Rahman, "MultiResUNet: Rethinking the U-Net architecture for multimodal biomedical image segmentation," Neural Networks, Vol. 121, 74-87, Jan. 2020.
doi:10.1016/j.neunet.2019.08.025

12. Fahad, S. K. Ahammad and Abdulsamad Ebrahim Yahya, "Inflectional review of deep learning on natural language processing," 2018 International Conference on Smart Computing and Electronic Enterprise (ICSCEE), Shah Alam, Malaysia, Jul. 11-12 2018.

13. Wang, Yingxu, "Cognitive foundations of knowledge science and deep knowledge learning by cognitive robots," 2017 IEEE 16th International Conference on Cognitive Informatics & Cognitive Computing (ICCI), 5, 2017.
doi:10.1109/ICCI-CC.2017.8109802

14. Jafar-Zanjani, Samad, Mohammad Mahdi Salary, Dat Huynh, Ehsan Elhamifar, and Hossein Mosallaei, "Tco-based active dielectric metasurfaces design by conditional generative adversarial networks," Advanced Theory and Simulations, Vol. 4, No. 2, Feb. 2021.
doi:10.1002/adts.202000196

15. Bae, Munseong, Jaegang Jo, Myunghoo Lee, Joonho Kang, Svetlana V Boriskina, and Haejun Chung, "Inverse design and optical vortex manipulation for thin-film absorption enhancement," Nanophotonics, Vol. 12, No. 22, 4239–4254, 2023.

16. Kudyshev, Zhaxylyk A., Demid Sychev, Zachariah Martin, Omer Yesilyurt, Simeon I. Bogdanov, Xiaohui Xu, Pei-Gang Chen, Alexander V. Kildishev, Alexandra Boltasseva, and Vladimir M. Shalaev, "Machine learning assisted quantum super-resolution microscopy," Nature Communications, Vol. 14, No. 1, Aug. 10 2023.
doi:10.1038/s41467-023-40506-4

17. Qi, Shutong, Yinpeng Wang, Yongzhong Li, Xuan Wu, Qiang Ren, and Yi Ren, "Two-dimensional electromagnetic solver based on deep learning technique," IEEE Journal on Multiscale and Multiphysics Computational Techniques, Vol. 5, 83-88, 2020.
doi:10.1109/JMMCT.2020.2995811

18. Guo, Rui, Zhichao Lin, Tao Shan, Maokun Li, Fan Yang, Shenheng Xu, and Aria Abubakar, "Solving combined field integral equation with deep neural network for 2-d conducting object," IEEE Antennas and Wireless Propagation Letters, Vol. 20, No. 4, 538-542, Apr. 2021.
doi:10.1109/LAWP.2021.3056460

19. Massa, Andrea, Davide Marcantonio, Xudong Chen, Maokun Li, and Marco Salucci, "Dnns as applied to electromagnetics, antennas, and propagationa review," IEEE Antennas and Wireless Propagation Letters, Vol. 18, No. 11, 2225-2229, Nov. 2019.
doi:10.1109/LAWP.2019.2916369

20. Alzahed, Abdelelah M., Said M. Mikki, and Yahia M. M. Antar, "Nonlinear mutual coupling compensation operator design using a novel electromagnetic machine learning paradigm," IEEE Antennas and Wireless Propagation Letters, Vol. 18, No. 5, 861-865, May 2019.
doi:10.1109/LAWP.2019.2903787

21. Giannakis, Iraklis, Antonios Giannopoulos, and Craig Warren, "A machine learning-based fast-forward solver for ground penetrating radar with application to full-waveform inversion," IEEE Transactions on Geoscience and Remote Sensing, Vol. 57, No. 7, 4417-4426, Jul. 2019.
doi:10.1109/TGRS.2019.2891206

22. Chen, Sizhe, Haipeng Wang, Feng Xu, and Ya-Qiu Jin, "Target classification using the deep convolutional networks for sar images," IEEE Transactions on Geoscience and Remote Sensing, Vol. 54, No. 8, 4806-4817, Aug. 2016.
doi:10.1109/TGRS.2016.2551720

23. Lagaris, IE, A Likas, and DI Fotiadis, "Artificial neural networks for solving ordinary and partial differential equations," IEEE Transactions on Neural Networks, Vol. 9, No. 5, 987-1000, Sep. 1998.
doi:10.1109/72.712178

24. Lagaris, IE, AC Likas, and DG Papageorgiou, "Neural-network methods for boundary value problems with irregular boundaries," IEEE Transactions on Neural Networks, Vol. 11, No. 5, 1041-1049, Sep. 2000.
doi:10.1109/72.870037

25. McFall, Kevin Stanley and James Robert Mahan, "Artificial neural network method for solution of boundary value problems with exact satisfaction of arbitrary boundary conditions," IEEE Transactions on Neural Networks, Vol. 20, No. 8, 1221-1233, Aug. 2009.
doi:10.1109/TNN.2009.2020735

26. Anitescu, Cosmin, Elena Atroshchenko, Naif Alajlan, and Timon Rabczuk, "Artificial neural network methods for the solution of second order boundary value problems," Cmc-computers Materials & Continua, Vol. 59, No. 1, 345-359, 2019.
doi:10.32604/cmc.2019.06641

27. Abdolrazzaghi, Mohammad, Soheil Hashemy, and Ali Abdolali, "Fast-forward solver for inhomogeneous media using machine learning methods: artificial neural network, support vector machine and fuzzy logic," Neural Computing & Applications, Vol. 29, No. 12, 1583-1591, Jun. 2018.
doi:10.1007/s00521-016-2694-9

28. Nitta, T, "An extension of the back-propagation algorithm to complex numbers," Neural Networks, Vol. 10, No. 8, 1391-1415, Nov. 1997.
doi:10.1016/S0893-6080(97)00036-1