This PhD project lies within the field of Non-Destructive Testing (NDT), which encompasses a range of techniques used to detect defects in structures (cables, materials, components) without causing any damage. Diagnostics rely on physical measurements (e.g., reflectometry, ultrasound), whose interpretation requires solving inverse problems, which are often ill-posed.

Classical approaches based on iterative algorithms are accurate but computationally expensive, and difficult to embed for near-sensor, real-time analysis. The proposed research aims to overcome these limitations by exploring physics-informed deep learning approaches, in particular:

* Neural networks inspired by traditional iterative algorithms (algorithm unrolling),
* PINNs (Physics-Informed Neural Networks) that incorporate physical laws directly into the learning process,
* Differentiable models that simulate physical measurements (especially reflectometry).

The goal is to develop interpretable deep models in a modular framework for NDT, that can run on embedded systems. The main case study will focus on electrical cables (TDR/FDR), with possible extensions to other NDT modalities such as ultrasound. The thesis combines optimization, learning, and physical modeling, and is intended for a candidate interested in interdisciplinary research across engineering sciences, applied mathematics, and artificial intelligence.