Subject Ph. D.

Biophotonics and biomedical optics are major fields of research involved in the development of innovative medical methods and devices [1] that enable non-invasive in vivo characterisation of biological tissues. The SpectroLive device developed at CRAN, supported by the Infra+ PhotoVivo platform, has enabled the acquisition of one of the richest published clinical spectroscopic databases known to date in the field of skin cancer. As part of the implementation of tissue optical spectro-imaging methods for the diagnosis of human skin cancers, the development of reliable methods for the in vivo estimation of optical parameters (absorption, diffusion), which are discriminating biomarkers for the identification of pathologies, based on these spectroscopic data, is a major challenge and a very active area of research.

Light-matter interactions that govern the forward sensing process for spectra acquisitions are modeled by the radiative transfer equation, which describes the evolution of the radiation energy u depending on the absorption and diffusion coefficients (pa,ps) of the tissue. This project is concerned with the corresponding inverse PDE problem, where one aims at recovering these optical parameters from given measurements y = F(u) (i.e. the observed spectra). Physics-informed neural networks (PINNs) have recently emerged as an efficient way of tackling such inverse problems [2], combining the predictive power of neural networks with the interpretability of underlying physics. They have in particular been used to solve the radiative transfer equations in some cases [3,4]. In [3], the authors propose to search for the unknown functions (u and pa in their case) as feedforward neural networks with parameters w=(wu, wa) that solve

(1) minimise with respect to w J(w) := ||D(w) ||² + || B(w) ||² + L( F(u(wu)), y ) + R(w),

where D and B are the differential operators representing the PDE and its boundary conditions respectively, and L and R are cost functions to be chosen depending on the problem of interest, modelling data fidelity and regularisation. In this case, the training data consists in collocation points over the definition domains of u and pa, that are used to compute the first two terms in the objective J.

The proposed PhD thesis aims at further investigating the use of such PINNs to invert the radiative transfer equation, in the context of estimating optical properties from the SpectroLive clinical data. It will address the following challenges :


⬢ extending the approach (1) to the joint recovery of both optical parameters pa and ps ;
⬢ adapting the model to handle the different spectroscopic modalities offered by the SpectroLive sensing process [1], namely diffuse reflectance and auto-fluorescence, which result in different boundary conditions, and different source terms for the PDE ;
⬢ designing data fidelity terms that are calibrated for SpectroLive, which e.g. entails handling variability and heterogeneity in the data. Robust alternatives to least-squares penalties, such as unbalanced optimal transport [5], will be considered.
⬢ providing theoretical guarantees on the convergence and generalisation error of the model (e.g. as a function of the amount of training data), following the guidelines provided by recent works [6,7]. Numerical experiments or experiments on optical phantoms will support this study.

References:

[1] Blondel et al. (2021) "Spatially-Resolved Multiply-Excited Autofluorescence and Diffuse Reflectance Spectroscopy: SpectroLive Medical Device for Skin In Vivo Optical Biopsy", Electronics, 10(3):243. ?hal-03380396? [2] Raissi et al. (2019) "Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations'', Journal of Computational Physics, 378, 686-707. [3] Mishra and Molinaro (2021). ''Physics informed neural networks for simulating radiative transfer'', Journal of Quantitative Spectroscopy & Radiative Transfer, 270, 107705. [4] Biswal et al. (2025). "Physics informed neural networks to solve radiative transfer equation in absorbing-scattering media'', Journal of Quantitative Spectroscopy & Radiative Transfer, 344, 109509. [5] Peyré et Cuturi. (2018) "Computational Optimal Transport : With Applications to Data Science'', Foundations and Trends in Machine Learning, 11(5-6), 355-607. ?hal-02411770? [6] Mishra and Molinaro (2023). ''Estimates on the generalization error of physics-informed neural networks for approximating PDEs'', IMA Journal of Numerical Analysis, 43, 1-43. [7] Doumèche et al. (2026). ''On the convergenve of PINNs'', Bernoulli, 2025, 31, 2127-2151. ?hal-04085519v2?

This PhD offer is provided by the ENACT AI Cluster and its partners. Find all ENACT PhD offers and actions on https://cluster-ia-enact.ai/.