volume | PIER Journals

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.

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

Dr. Mohammad Ahmad