Keywords – Non-linear and linear inverse problem, Waves scattering, Physics-assisted learning, Complex-Valued Neural Network, Generalizable models
Context – Inverse problems involve inferring unknown parameters or properties of a system from observed data. These problems are often ill-posed, meaning that solutions may not exist, be unique, or be stable to small variations in the data. Traditional, well-established numerical methods usually face challenges related to ill-posedness, sensitivity to noise, and computational cost, especially in complex systems. Recent deep learning approaches (Chen et al., 2020) have shown promising reconstruction performance. Still, most existing models are designed for a fixed acquisition setting, with a predetermined number and distribution of transmitters and receivers. As a result, their applicability remains limited: once the measurement configuration changes, the model often needs to be retrained from scratch. This project proposes to develop physics-assisted learning methods for inverse scattering, with the long-term goal of building models that are more robust, physically grounded, and less dependent on a single measurement setting.
Project description – In the first stage, the project will extend the existing unrolled framework (Zhang et al., 2023) for inverse scattering by incorporating physically meaningful features and, where beneficial, complex-valued neural representations to better handle wave data carrying amplitude and phase information. Complex-valued networks (Chiyan et al., 2022) are particularly relevant in wave-based inverse problems because the measured and reconstructed quantities are naturally complex; prior work (Guo et al., 2021) has shown that such models can improve the treatment of electromagnetic scattering data.
The central scientific question is not only how to improve reconstruction quality for a fixed setup, but also how to move toward a model less tied to a single transmitter/receiver configuration. To address this, the project will first investigate transfer learning (Gilton et al., 2021) as a practical and immediately implementable strategy: starting from a trained unrolled model, can one adapt it efficiently to nearby measurement settings without retraining from scratch? In a second stage, the project will use the insights from this first step to explore more general frameworks, potentially inspired by operator learning and variable-input neural architectures (Cheng et al., 2025), to handle varying numbers and distributions of transmitters and receivers in a unified way. This direction is consistent with the broader move in inverse scattering toward models that learn mappings between fields and unknown distributions rather than memorizing one fixed data layout.
Supervision – Marc Lambert, Chargé de recherche CNRS, Marc.Lambert@centralesupelec.fr ;
Yarui Zhang, Associate Professor, SATIE, ENS Paris-Saclay, yarui.zhang@ens-paris-saclay.fr.
Candidate profile and required skills – A scientific background in engineering/Master’s level (M2) with knowledge of waves and propagation and/or direct/inverse problem solving and/or deep learning is required. Knowledge of Python is a plus. Autonomy, perseverance, creativity, and a critical eye for the methods developed and the results obtained are also essential qualities for the successful completion of the thesis.
References :
X. Chen, Z. Wei, M. Li, et al. A review of deep learning approaches for inverse scattering problems (invited review), Progress In Electromagnetics Research, 167, 67-81, 2020.
Y. Cheng C. Tian, H. Wang, et al. Generalizable neural electromagnetic inverse scattering, arXiv 2506.21349, 2025.
L. Chiyan, H. Hideyuki et G. Shangce. « Complex-Valued Neural Networks : A Comprehensive Survey ». IEEE/CAA Journal of Automatica Sinica 9, 2022
D. Gilton, G. Ongie, and R. Willett, Model adaptation for inverse problems in imaging, IEEE Transactions on Computational Imaging, 7,
661-674, 2021
L. Guo, G. Song et H. Wu. « Complex-Valued Pix2pixDeep Neural Network for Nonlinear Electromagnetic Inverse Scattering ».
Electronics, 10, 2021
Y. Zhang. « Non-linear electromagnetic imaging: from sparsity-preserving wavelet-based algorithms to deep learning ». Theses. Université Paris-Saclay, 2022 (https://theses.hal.science/tel-04370248v1)
