Physics-informed Deep Learning to Solve 2D Electromagnetic Scattering Problems

Authors

  • Ji-Yuan Wang School of Integrated Circuit and Electronics Beijing Institute of Technology, Beijing, 100081, China https://orcid.org/0009-0003-4536-5265
  • Xiao-Min Pan School of Cyberspace Science and Technology Beijing Institute of Technology, Beijing, 100081, China

DOI:

https://doi.org/10.13052/2023.ACES.J.380905

Keywords:

Electromagnetic scattering, physics-informed deep learning, the method of moments

Abstract

The utilization of physics-informed deep learning (PI-DL) methodologies provides an approach to augment the predictive capabilities of deep learning (DL) models by constraining them with known physical principles. We utilize a PI-DL model called the deep operator network (DeepONet) to solve two-dimensional (2D) electromagnetic (EM) scattering problems. Numerical results demonstrate that the discrepancy between the DeepONet and conventional method of moments (MoM) is small, while maintaining computational efficiency.

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Author Biographies

Ji-Yuan Wang, School of Integrated Circuit and Electronics Beijing Institute of Technology, Beijing, 100081, China

Ji-Yuan Wang received the B.S. degree from Communication University of China, Beijing, China, in 2021. He is currently pursuing the M.S. degree with the School of Integrated Circuit and Electronics, Beijing Institute of Technology, Beijing. His current research interests include deep learning and computational electromagnetics.

Xiao-Min Pan, School of Cyberspace Science and Technology Beijing Institute of Technology, Beijing, 100081, China

Xiao-Min Pan received the B.S. and M.S. degrees from Wuhan University, Wuhan, China, in 2000 and 2003, respectively, and the Ph.D. degree from the Institute of Electronics, Chinese Academy of Sciences, Beijing, China, in 2006. He is currently a professor with the School of Cyberspace Science and Technology, Beijing Institute of Technology, Beijing. He has authored or coauthored over 60 papers in refereed journals. His current research interests include high-performance methods in computational electromagnetics, artificial intelligence in electromagnetics, and electromagnetic compatibility analysis of complex systems.

Prof. Pan was the third recipient of the First Prize of Beijing Science and Technology Awards in 2011, the recipient of the New Century Excellent Talents in University in 2012 and of Young Elite Talents in Beijing in 2012. He received the Ulrich L. Rohde Innovative Conference Paper Award in 2016 and several other international academic awards. He served as a technical program committee co-chair, special sessions co-chairs, and technical program committee member for several international conferences and symposiums.

References

W. C. Chew, M. S. Tong, and B. Hu, “Integral equation methods for electromagnetic and elastic waves,” Synthesis Lectures on Computational Electromagnetics, vol. 3, no. 1, pp. 1–241, 2008.

D.-M. Yu, X. Ye, X.-M. Pan, and X.-Q. Sheng, “Fourier bases-expansion for three-dimensional electromagnetic inverse scattering problems,” IEEE Geoscience and Remote Sensing Letters, vol. 19, pp. 1–5, 2022.

X. Chen, Computational Methods for Electromagnetic Inverse Scattering, John Wiley & Sons, 2018.

Y.-N. Liu and X.-M. Pan, “Solution of volume-surface integral equation accelerated by MLFMA and skeletonization,” IEEE Transactions on Antennas and Propagation, vol. 70, no. 7, pp. 6078–6083, 2022.

L. Li, L. G. Wang, F. L. Teixeira, C. Liu, A. Nehorai, and T. J. Cui, “DeepNIS: Deep neural network for nonlinear electromagnetic inverse scattering,” IEEE Transactions on Antennas and Propagation, vol. 67, no. 3, pp. 1819–1825, 2018.

S. Qi, Y. Wang, Y. Li, X. Wu, Q. Ren, and Y. Ren, “Two-dimensional electromagnetic solver based on deep learning technique,” IEEE Journal on Multiscale and Multiphysics Computational Techniques, vol. 5, pp. 83–88, 2020.

Z. Ma, K. Xu, R. Song, C.-F. Wang, and X. Chen, “Learning-based fast electromagnetic scattering solver through generative adversarial network,” IEEE Transactions on Antennas and Propagation, vol. 69, no. 4, pp. 2194–2208, 2020.

R. Guo, T. Shan, X. Song, M. Li, F. Yang, S. Xu, and A. Abubakar, “Physics embedded deep neural network for solving volume integral equation: 2-D case,” IEEE Transactions on Antennas and Propagation, vol. 70, no. 8, pp. 6135–6147, 2021.

Y. Hu, Y. Jin, X. Wu, and J. Chen, “A theory-guided deep neural network for time domain electromagnetic simulation and inversion using a differentiable programming platform,” IEEE Transactions on Antennas and Propagation, vol. 70, no. 1, pp. 767–772, 2021.

B.-W. Xue, D. Wu, B.-Y. Song, R. Guo, X.-M. Pan, M.-K. Li, and X.-Q. Sheng, “U-net conjugate gradient solution of electromagnetic scattering from dielectric objects,” in 2021 International Applied Computational Electromagnetics Society (ACES-China) Symposium, pp. 1–2, IEEE,2021.

Z. Hao, S. Liu, Y. Zhang, C. Ying, Y. Feng, H. Su, and J. Zhu, “Physics-informed machine learning: a survey on problems, methods and applications,” arXiv preprint arXiv:2211.08064, 2023.

P. Zhang, Y. Hu, Y. Jin, S. Deng, X. Wu, and J. Chen, “A Maxwell’s equations based deep learning method for time domain electromagnetic simulations,” IEEE Journal on Multiscale and Multiphysics Computational Techniques, vol. 6, pp. 35–40, 2021.

L. Lu, X. Meng, Z. Mao, and G. E. Karniadakis, “DeepXDE: A deep learning library for solving differential equations,” SIAM Review, vol. 63, no. 1, pp. 208–228, 2021.

S. Lanthaler, S. Mishra, and G. E. Karniadakis, “Error estimates for deeponets: A deep learning framework in infinite dimensions,” Transactions of Mathematics and Its Applications, vol. 6, no. 1, p. tnac001, 2022.

L. Lu, P. Jin, G. Pang, Z. Zhang, and G. E. Karniadakis, “Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators,” Nature Machine Intelligence, vol. 3, no. 3, pp. 218–229, 2021.

T. Chen and H. Chen, “Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems,” IEEE Transactions on Neural Networks, vol. 6, no. 4, pp. 911–917, 1995.

C. Trabelsi, O. Bilaniuk, Y. Zhang, D. Serdyuk, S. Subramanian, J. F. Santos, S. Mehri, N. Rostamzadeh, Y. Bengio, and C. J. Pal, “Deep complex networks,” arXiv preprint arXiv:1705.09792,2017.

X.-M. Pan, B.-Y. Song, D. Wu, G. Wei, and X.-Q. Sheng, “On phase information for deep neural networks to solve full-wave nonlinear inverse scattering problems,” IEEE Antennas and Wireless Propagation Letters, vol. 20, no. 10, pp. 1903–1907, 2021.

N. Ketkar, J. Moolayil, N. Ketkar, and J. Moolayil, “Introduction to pytorch,” Deep Learning with Python: Learn Best Practices of Deep Learning Models with PyTorch, pp. 27–91, 2021.

Y. Saad and M. H. Schultz, “GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems,” SIAM Journal on Scientific and Statistical Computing, vol. 7, no. 3, pp. 856–869, 1986.

The MNIST database can be downloaded at http://yann.lecun.com/exdb/mnist/.

D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” arXiv preprint arXiv:1412.6980, 2014.

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Published

2023-09-30

How to Cite

[1]
J.-Y. . Wang and X.-M. . Pan, “Physics-informed Deep Learning to Solve 2D Electromagnetic Scattering Problems”, ACES Journal, vol. 38, no. 09, pp. 667–673, Sep. 2023.

Issue

2023: Vol 38 Iss 9

Section

Special Issue on ACES-China 2022 Conference