Wasserstein Geodesic

Wasserstein geodesics represent the shortest paths between probability distributions in a space where distance is measured by the Wasserstein metric, reflecting the optimal transport cost between distributions. Current research focuses on efficiently computing these geodesics, particularly through novel algorithms and neural network architectures like GeONet, which learn to approximate the geodesic directly. This work finds applications in diverse fields, including data augmentation for improved model robustness, conditional distribution generation, and swarm control optimization, by leveraging the geometric properties of Wasserstein space to solve challenging problems in machine learning and beyond. The development of faster and more accurate methods for computing and utilizing Wasserstein geodesics is driving significant advancements in these areas.