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Model-based deep learning for efficient electromagnetic modelling of high-dimensional frequency selective surfaces

26 Octobre 2023

Catégorie : Stagiaire

M2 Internship at INSA Rennes


1 Objectives

The main objective of the internship is to create a neural-network-based electromagnetic (EM) model of an frequency selective surface (FSS) capable of predicting its frequency response (S-parameters) from the FSS geometry and angle of incidence (AoI) of the EM wave over the surface, while avoiding heavy full-wave simulations. Physical insight will be incorporated into the structure of the proposed neural network by the use of equivalent circuits as an intermediate step in the prediction process. As a consequence, the developed method is model-based. A second objective of this project is to verify and clearly demonstrate the advantage of using this model-based strategy using physical insight. To do so, another neural network will be developed, which will make predictions of the S-parameters based directly on the geometric parameters of the FSS without using any equivalent circuit. An exhaustive comparison of the performances attained by both approaches will be carried out.


2 Novelty

Model-based deep learning (DL) has been introduced recently as a trade-off between signal processing and machine learning [1] and led to promising results in various fields of signal processing for the physical layer [2–6]. On the other hand, classical machine learning methods have been applied to the design of radio-frequency (RF) structures for some time [7–11]. However, these papers do not take advantage of the underlying physics to build of model-based learning methods, and therefore still require heavy full-wave simulations. This project will be therefore the first time that model-based learning is applied to the characterization of RF devices.


3 Organization

It is envisioned to divide the intership in four stages (durations are indicative):

1. Familiarization with the problem (3 weeks) • The student will begin to work with the already existing code with the objective of getting a deep understanding of its functioning, the generation of the train and test datasets and the choice of the configuration parameters.

2. Verification of the advantage of model-based solutions (8 weeks) • The student will develop a neural network that makes predictions about the S-parameters without putting any physical insight into the model. He/she will run tests to compare the performance of this approach with the one that makes use of physical insight.

3. Integration of the angle of incidence (AoI) as an input parameter (8 weeks) 1 • The student will expand the model with physical insight to take into account the AoI of the waves over the FSS.

4. Close up (5 weeks) • The student will participate in the elaboration of a manuscript with the obtained results and he/she will also document and package all the developed code. Regarding the mentoring of the student, Luc Le Magoarou will be in charge of providing the support regarding the neural network theory aspects, while Lucas Polo-L´opez and Mar´ıa Garc´ıa-Vigueras will provide guidance regarding the EM modelling aspects. Moreover, all the three participants are well experienced in software developing and they will be able to help the student with any problems that may arise regarding this subject.


4 Potential outcomes

Reducing the computational burden of EM simulations with many degrees of freedom is a subject of great interest for many research fields involving electromagnetics. In fact, this DL-assisted EM modelling is one of the objectives of the future EM modelling platform that will be developed within the QOSC platform of IETR. The results of this project could be leveraged well beyond the scope of FSS, to be integrated in the platform. In terms of dissemination, a paper submission at the end of the internship is envisioned.


5 Logistics

The internship will be hosted in the SIGNAL and SURFWAVE teams of the IETR (on the campus of INSA Rennes), for a duration of six months starting between January and March of 2024.

Students in their final year (M2/PFE) with a background/interest in electromagnetics, signal processing, machine learning and applied mathematics are encouraged to apply by sending an email to



[1] Nir Shlezinger, Jay Whang, Yonina C Eldar, and Alexandros G Dimakis. Model-based deep learning. Proceedings of the IEEE, 2023.

[2] Taha Yassine and Luc Le Magoarou. mpnet: variable depth unfolded neural network for massive mimo channel estimation. IEEE Transactions on Wireless Communications, 21(7):5703–5714, 2022.

[3] Nhan Thanh Nguyen, Mengyuan Ma, Nir Shlezinger, Yonina C Eldar, AL Swindlehurst, and Markku Juntti. Deep unfolding hybrid beamforming designs for thz massive mimo systems. arXiv preprint arXiv:2302.12041, 2023.

[4] Jérôme Sol, Hugo Prod’Homme, Luc Le Magoarou, and Philipp del Hougne. Experimentally realized physical-model-based wave control in metasurface-programmable complex media. arXiv preprint arXiv:2308.02349, 2023.

[5] José Miguel Mateos-Ramos, Christian H¨ager, Musa Furkan Keskin, Luc Le Magoarou, and Henk Wymeersch. Model-based end-to-end learning for multi-target integrated sensing and communication. arXiv preprint arXiv:2307.04111, 2023.

[6] Baptiste Chatelier, Luc Le Magoarou, Vincent Corlay, and Matthieu Crussière. Model-based learning for location-to-channel mapping. arXiv preprint arXiv:2308.14370, 2023.

[7] Daniel R. Prado, Jesus A. Lopez-Fernandez, Guillermo Barquero, Manuel Arrebola, and Fernando Las-Heras. Fast and Accurate Modeling of Dual-Polarized Reflectarray Unit Cells Using Support Vector Machines. IEEE Transactions on Antennas and Propagation, 66(3):1258–1270, March 2018.

[8] Parinaz Naseri and Sean V. Hum. A Machine Learning-Based Approach to Synthesize Multilayer Metasurfaces. In 2020 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting, pages 933–934, Montreal, QC, Canada, July 2020. IEEE.

[9] Tian Lin and Yu Zhu. Beamforming Design for Large-Scale Antenna Arrays Using Deep Learning. IEEE Wireless Communications Letters, 9(1):103–107, January 2020.

[10] Sotirios K. Goudos, Panagiotis D. Diamantoulakis, Mohammad A. Matin, Panagiotis Sarigiannidis, Shaohua Wan, and George K. Karagiannidis. Design of Antennas through Artificial Intelligence: State of the Art and Challenges. IEEE Communications Magazine, 60(12):96–102, December 2022.

[11] Amirhossein Fallah, Ahmad Kalhor, and Leila Yousefi. Developing a carpet cloak operating for a wide range of incident angles using a deep neural network and PSO algorithm. Scientific Reports, 13(1):670, January 2023.