The goal of this project is to shift the dominant paradigm of learning-based computer vision: instead of systems attempting to replace human interpretation by providing predictions, we will develop approaches to assist experts in identifying and analyzing patterns. Indeed, while the success of deep learning on visual data is undeniable, applications are often limited to the supervised learning scenario where the algorithm tries to infer a label for a new image based on the annotations made by experts in a reference dataset. In contrast, we will take as input images without any annotation, automatically identify consistent patterns and model their variation and evolution, so that an expert can more easily analyze them. I will introduce and develop the concept of visual structures. Their key features will be their interpretability, in terms of correspondences, deformations, or properties of the observed images, and their ability to incorporate prior knowledge about the data and expert feedback. I propose two complementary approaches to formally define and identify visual structures: one based on analyzing correspondences, the other on learning interpretable image models. We will develop visual structures in two domains in which breakthrough progress will open up new scientific discoveries: historical documents and Earth imagery. For example, from temporal series of multispectral Earth images, we will identify types of moving objects, areas with different types of vegetation or constructions, and model the evolution of their characteristics, which may correspond to changes in their activity or life cycle. Ultimately, experts will still be needed to select relevant visual structures and perform analysis, but DISCOVER will revolutionize their work, trivializing tedious annotation tasks and even allowing them to work on issues they would have been hard-pressed to identify in the raw data.

Interacting particle- or agent-based systems are ubiquitous in science. They arise in an extremely wide variety of applications including materials science, biology, economics and social sciences. Several mathematical models exist to account for the evolution of such systems at different scales, among which stand stochastic differential equations, optimal transport problems, Fokker-Planck equations or mean-field games systems. However, all of them suffer from severe limitations when it comes to the simulation of high-dimensional problems, the high-dimensionality character coming either from the large number of particles or agents in the system, the high amount of features of each agent or particle or the huge quantity of parameters entering the model. The objective of this project is to provide a new mathematical framework for the development and analysis of efficient and accurate numerical methods for the simulation of high-dimensional particle or agent systems, stemming from applications in materials science and stochastic game theory. The main challenges which will be addressed in this project are: -sparse optimization problems for multi-marginal optimal transport problems, using moment constraints; -numerical resolution of high-dimensional partial differential equations, with stochastic iterative algorithms; -efficient approximation of parametric stochastic differential equations, by means of reduced-order modeling approaches. The potential impacts of the project are huge: making possible such extreme-scale simulations will enable to gain precious insights on the predictive power of agent- or particle-based models, with applications in various fields, such as quantum chemistry, molecular dynamics, crowd motion or urban traffic.

In current "conventional" agricultural practices, most farmers depend on synthetic fertilizers and nutrients extracted during harvests are seldom brought back to the soil. This open-circuit organization of food systems induces the prospect of phosphate shortage and consumes large amounts of abiotic resources and energy to generate fertilizers or process nutrients once they end up in sewage. Such a linear and extractive system, together with current fertilizer application methods, has incurred great social and environmental costs around the world, leading to significant biodiversity loss, soil erosion and salinisation as well as nutrient leaching. Finally, animal-based diets in the largest economies further increase the pressure on food systems as feeding animals inflates land and nutrient use. Source separation of organic matter and its recovery are likely to be critical for the long-term sustainability of the agri-food and waste-management systems in an increasingly urban world. Indeed, the transformation of kitchen or green waste and human excreta can provide invaluable resources such as compost, fertilizers, or energy and eventually remove the need for synthetic fertilizers. This project will develop prospective scenarios for nutrient recovery and assess how far they can bring the agri-food system on the path to circularity. Using complex networks and systems methods, we will convert and analyze existing datasets to generate logistics networks associated to these scenarios. These networks will model the fluxes of organic matter between sources (habitations), processing or storage locations, and sinks (parcels). We will also assess the impact of dietary changes and low-fertilizer or agro-ecological practices compared to business-as-usual situations. This will enable us to evaluate the technical feasibility of these recovery scenarios and quantify how much they improve agri-food sustainability and can help local actors tackle their socio-ecological transition.

Clays are nanostructured materials that contain adsorbed water, i.e., water molecules interacting with the solid skeleton. Clay hydration and dehydration is well known to induce important deformations of the material that may end up to instabilities such as desiccation cracking of soils in dry conditions. Cracking of clay-rich rocks can be detrimental (nuclear waste or CO2 storage) or beneficial (oil and gas recovery). Clay desiccation can originate from heating since an increment of temperature induces dehydration and shrinkage. Thermal stimulation is considered as a potential alternative to hydraulic fracturing for shale oil and gas recovery from clay-rich deposits. But the technique is exploratory and its feasibility has to be demonstrated. In this project, we will investigate in detail the physics of thermal expansion of adsorbing microporous media, in particular that of clays, and ultimately assess the feasibility of thermal stimulation of shales. Adsorption in microporous solids is known to induce unusual deformations that can be understood at the molecular scale and captured by thermodynamic integration. Adsorption can induce both shrinkage and swelling depending on the molecular interactions between the fluid and the solid. Accordingly the thermal expansion of adsorbing media can be complex and we propose in this project to study it from the molecular scale to get insight into the physical mechanisms involved. We will investigate various model situations by molecular simulation and derive analytical description of the phenomena from thermodynamics. We will pay a special attention to the physical mechanisms that are relevant for clays. Clays are complex multi-scale materials in which the nanostructure is made of planar micropores where adsorption is structured in layers and induces a swelling orthogonal to the layers, with sharp transitions in function of water chemical potential and temperature. In contrast, macroscopic experiments on clays show continuous thermal deformation with both contraction and expansion, depending on the pre-consolidation state of the material and on the temperature. In this project, we will investigate the thermal expansion of clays from the molecular scale to the macroscopic scale and bridge the gap between the two scales. A fine understanding of the behavior of clay will enable to develop a thermo-hydro-mechanical constitutive modeling with a good predictive ability over a wide range of temperatures and in-situ stresses, relevant for application to thermal stimulation of shales. Finally, this constitutive modeling will serve as a basis for a stability analysis of shale reservoirs and thus to determine the conditions favorable to desiccation cracking. This project is structured as a comprehensive multi-scale approach that involves molecular simulation, thermodynamics and statistical physics, mechanical homogenization and rock mechanics. This project will provide interesting scientific results for the understanding of microporous solids in general and of clays in particular. The project will also have a relevant impact for applications in emerging geotechnical issues involving clays, especially for shale oil and gas recovery.