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Generalised Optimal Transport and Applications – GOTA
This project deals with some generalizations of Optimal Transport problems and their applications. We plan to tackle three main topics: multi-marginal optimal transport (and applications in risk measures and quantum chemistry), multi-population models in urban planning and entropic optimal transpor
Optimal Transport: Theory and Applications to cosmological Reconstruction and Image processing – OTARIE
Optimal transport is a mathematical subject connecting the fields of optimization, partial differential equations, and dynamical systems in both finite and infinite dimensions. The basic problem of optimal transport is to find a transport plan that connects two given distributions of mass and minimi
Theory and Applications of the Geometry of Entropy Regularized Optimal Transport – THEATRE
Optimal transport, including its entropic regularization, plays an increasing role in our understanding of optimization schemes arising from machine learning problems. The good behavior of such optimization problems and the resulting algorithms are shrewdly related to the geometry induced by the met
Data-driven optimization in synchromodal freight transportation networks – CRC Lab
Freight transport networks aim to make the transport of goods from their production facilities to their end customers as efficient as possible. The use of logistics hubs and the pooling of goods flows make it possible to improve performance, both in terms of service and cost control, and to limit th
Regression with Optimal Transport for Computer Graphics and Vision – ROOT
ROOT will develop numerical methods for solving important problems in computer graphics and vision via the optimal mass transport theory. These problems relate to histograms, and can be advantageously written and solved via regressions with loss functions involving optimal transport. These problems
Geometry and optimal measure transportation – GMT
The Ricci curvature plays an important role in Geometry and has lately been linked with the Optimal transportation theory. First by G.~Perelman's proof of the Poincaré conjecture using the Ricci-flow and citing Bakry and Emery's work on ``Diffusions hypercontractives''. Secondly by a serie of pa
Systematic Machine Learning Approach for Revolutionary Traffic Optimization in Urban Transportation Engineering – SMART-ROUTE
Rapid growth in the demand for urban transportation networks has underlined the urgent need for sophisticated management of multimodal transportation networks due to the significant costs associated with traffic congestion and CO2 emissions. Addressing these challenges requires a dual focus: allevia
Optimal Transport and Image Multiphysics – TOMMI
Interpolating between two images is an old problem from image analysis, which finds applications for example to recover lost or damaged data in experiments films. It is also used in order to determine in which state the studied system could have been at some time when no observations were made. Imag
Earth Observation with Optimal Transport for Artificial Intelligence – OTTOPIA
Earth Observation, whether it be by satellites, airborne captors or drones, allows a better understanding of the dynamics of environmental systems or our human society. It is a decisive tool to measure the impact of mankind on earth. In the last 50 years, the fast development of spatial missions and
OptimAl Transport for MachIne Learning – OATMIL
In our era of steady data deluge, there is no doubt that the design of efficient techniques to extract knowledge from massive data collections or data streams has become a fundamental scientific and technological challenge bearing immense opportunities, both industrial and societal. As such, it is n
