Optimal Transport and flows in probability space
Subspace Detours Meet Gromov-Wasserstein
Bonet Clément, Vayer Titouan, Courty Nicolas, Septier François, Drumetz Lucas
Algorithms, MDPI, 2021, Special Issue Optimal Transport: Algorithms and Applications, 14, pp.1-29.
https://arxiv.org/abs/2110.10932
Sliced-Wasserstein Gradient Flows
Bonet, C., Courty, N., Septier, F., & Drumetz, L. (2022). Efficient gradient flows in sliced-Wasserstein space. Transactions on Machine Learning Research.
Also presented (Spotlight) at the NeurIPS Workshop on Optimal Transport and Machine Learning (OTML)
https://otml2021.github.io/papers
Sliced Optimal Transport and Riemannian Geometry
Bonet, C., Berg, P., Courty, N., Septier, F., Drumetz, L., & Pham, M. T. (2022, September). Spherical Sliced-Wasserstein. In The Eleventh International Conference on Learning Representations.
Bonet, C., Chapel, L., Drumetz, L., & Courty, N. (2023, September). Hyperbolic sliced-wasserstein via geodesic and horospherical projections. In Topological, Algebraic and Geometric Learning Workshops 2023 (pp. 334-370). PMLR.
Bonet, C., Malézieux, B., Rakotomamonjy, A., Drumetz, L., Moreau, T., Kowalski, M., & Courty, N. (2023, July). Sliced-Wasserstein on symmetric positive definite matrices for M/EEG signals. In International Conference on Machine Learning (pp. 2777-2805). PMLR.
Sliced and Unbalanced Optimal Transport
Séjourné, T., Bonet, C., Fatras, K., Nadjahi, K., & Courty, N. (2023). Unbalanced Optimal Transport meets Sliced-Wasserstein. arXiv preprint arXiv:2306.07176.
Fast Optimal Transport through Sliced Wasserstein Generalized Geodesics
Mahey, G., Chapel, L., Gasso, G., Bonet, C., & Courty, N. (2024). Fast Optimal Transport through Sliced Generalized Wasserstein Geodesics. Advances in Neural Information Processing Systems, 36.
Super-resolution in Physical Imaging
Post Processing Sparse And Instantaneous 2D Velocity Fields Using Physics-Informed Neural Networks
Di Carlo, Diego and Heitz, Dominique and Corpetti, Thomas,
20th international symposium on applications of laser techniques to fluid mechanic, Lisbon, 2022
Dynamical formulation of the learning process
Turning Normalizing Flows into Monge Maps with Geodesic Gaussian Preserving Flows
Guillaume Morel, Lucas Drumetz, Simon Benaïchouche, Nicolas Courty, François Rousseau
Transactions on Machine Learning Research, 2023.
https://arxiv.org/abs/2209.10873
Also presented in 2022 at NeurIPS workshop “The symbiosis of deep learning and differential equations II”: https://nips.cc/virtual/2022/59912
