The rapid development of space systems and sensors for Earth and planetary observation now provides access to numerous geophysical, geochemical, and biophysical parameters at high spatial and temporal resolution. Such infrastructures are essential for understanding Earth’s changing climate as well as the environments and potential habitability of Mars and the Moon. These analyses rely on integrating observations through data assimilation and model inversion, key components of digital twin technologies for Earth and Space (E&S) science supported by ESA and NASA.

This PhD project aims to develop new learning and algorithmic foundations in this E&S context, involving massive data processing, uncertainty quantification, and decision making. We will address model inversion and assimilation of high-dimensional satellite data using deep generative and conditional diffusion models for Bayesian inference. These developments will also pave the way for optimal experimental design in the conception of new airborne or satellite sensors. 

Next-generation Bayesian inference with generative Artificial Intelligence.

The Bayesian framework is particularly suited to inverse problems in remote sensing, where the goal is to estimate an unknown parameter x from measurements y = A(x) + n, with A a forward physical model (or a measurement operator) and n additive noise. Such ill-posed problems require prior information to yield meaningful solutions. Traditionally, hand-crafted priors serve as regularization terms, but they are now being replaced by learned priors derived from deep generative models [PRO22]. Among these, diffusion models have shown outstanding performance in image generation [SSX+22], effectively learning complex parameter distributions. A generative model trained on observed instances can simulate new, unseen examples through a stochastic differential equation (SDE) framework that progressively transforms data into white noise and then reverses the process using a learned score function.

Beyond priors p(x), Bayesian inverse problems also require sampling from the posterior p(x|y), which remains computationally demanding. Conditional diffusion models have been proposed for this purpose, yet face challenges related to accuracy, cost, and the estimation of intractable conditional scores. Drawing on our experience with Bayesian inversion methods [KFD21, PDK+22], we propose reframing the Bayesian paradigm using conditional diffusion models, developing efficient data-driven samplers as alternatives to traditional density-based approaches (e.g., MCMC). We will investigate conditional diffusion formulations to identify the most suitable for complex E&S inference tasks. Two key innovations are targeted: (Task 1) increased amortization, enabling computation reuse across multiple observations—essential for large-scale planetary remote sensing—and (Task 2) efficient handling of multiple complementary measurements y₁…yₙ for sampling p(x|y₁…yₙ) at minimal cost.

These developments will be applied to Mars and Moon exploration, leveraging large multi-dimensional remote sensing datasets for surface material characterization (composition, texture, micro-roughness) and uncertainty quantification, with potential extensions to terrestrial and atmospheric studies. Together with partner laboratories, we will analyze measurements from ongoing (MRO, TGO/ExoMARS, MMX) and upcoming missions (LightShip-1) covering spatial, spectral, and angular dimensions in the visible and infrared domains.

The development of a diffusion-based framework will also pave the way to Bayesian Optimal Experimental Design (BOED) to optimize compact spectral imagers such as ImSPOC (Imaging SPectrometer On Chip) for embedded E&S applications, including atmospheric CO₂ and CH₄ monitoring. BOED will indeed be instrumental to determine the optimal interferogram sampling for maximum parameter sensitivity, accounting for latent variables such as acquisition geometry and atmospheric profiles.

Our vision, rooted in a multidisciplinary approach, is to advance both theoretical and practical aspects of E&S Science by integrating physics, statistics, and machine learning. Quantitative, rigorous performance assessment will be central to achieving balanced trade-offs between computational, inferential, and scientific objectives.

[KFD21] B. Kugler, F. Forbes, and S.  Douté. Fast Bayesian Inversion for high dimensional inverse problems. Statistics and Computing, 2021.

[PDK+22] Potin, S.M., Douté, S., Kugler, B., Forbes, F., 2022. The impact of asteroid shapes and topographies on their reflectance spectroscopy. Icarus 376, 114806.

[PRO22] Patel D., Ray D., Oberai A., 2022. Solution of physics-based Bayesian inverse problems with deep generative priors. Computer Methods in Applied Mechanics and Engineering 400.

[SSX+22] Yang Song, et al, Solving Inverse Problems in Medical Imaging with Score-

Based Generative Models. In 10th International Conference on Learning Representations

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For more Information about the topics and the co-financial partner (found by the lab!); contact Directeur de thèse - sylvain.doute@univ-grenoble-alpes.fr

Then, prepare a resume, a recent transcript and a reference letter from your M2 supervisor/ engineering school director and you will be ready to apply online before March 13th, 2026 Midnight Paris time!