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.

"Ecole des Ponts ParisTech has always been strongly involved in the various initiatives implemented by the European Commission in the field of the higher education. We have participated in the Socrates-Erasmus program (2000-2006) and in the Lifelong Learning program (2007-2013). In 2014 we have obtained the ""Erasmus Charter for higher education in 2014 -2020"", which have allowed us to contribute to the development of our international cooperation strategy.Strengthening the international reputation of our institution throughout Europe and leveraging the training opportunities offered to our student for improving their professional skills and employability were the main objectives of this project.As a result, this project involved a total of 31 participants, 25 of them for SMS mobilities and 6 for internship activities. Most of these mobilities have involved 2nd cycle students (22 students in total, which is equivalent to 88% of total student mobilities) who have completed their final and second year of study at one of our partners. About 50% of them have studied in the framework of a double degree program in countries such as Sweden and other Northern countries (the Netherlands, Finland, Norway), Germany and Italy. About 12% of the mobilities involved 1st cycle students.The level of activities sounds good to us since we could strengthen our cooperation with Northern European countries together with the number of mobilities. On top of that, we have enlarged the portfolio of learning options at our partners with additional fields of study. We are also happy with the number of 3 mobilities achieved at our longlasting partner in Italy.Regarding the funding of internships, we have stabilized the number of students to 4, which was one of our secondary objective."

"Ecole des Ponts ParisTech has always been heavily involved in the various initiatives implemented by the European Commission in the field of the higher education. We have participated in the Socrates-Erasmus program (2000-2006) and in the Lifelong Learning program (2007-2013). In 2014 we have obtained the ""Erasmus Charter for higher education in 2014 -2020"" which allowed us to participate in the new Erasmus + program. This participation contributes to the settlement and development of our strategy in the framework of international cooperation. The financial support obtained within the framework of this project hugely contributes to reach our objectives, which were the reinforcement of our international exposure by increasing our incoming mobility while insuring the training of the best students from our partner institutions with the French educational model. This project therefore involved a total of 53 participants, 48 of them for SMS mobilities and 5 for STA and STT activities (4 staff mobility for purposes of education and 1 for staff training). The most part of these mobilities are incoming flows, and have involved 2nd cycle students who have integrated our institution as a double degree or exchange student. As a result of activities we are satisfied with the outcomes because we have strengthened our cooperation in Argentina, Russia, Maghreb, Middle-East and Asia. This new program has allowed us to reinforce our academic cooperation beyond the European academic borders. We can say that we consolidated our institution's position as being a reference institution in its areas of excellence such as civil engineering, mechanical and material engineering, environment, transportation and urban planning, applied mathematics and economy. This new financing support has allowed us to consolidate and extend at the worldwide level the reputation and the visibility of our institution, which was one of our objectives to reach."