Kantorovich Potential

The Kantorovich potential is a central concept in optimal transport theory, used to find the most efficient way to "move" mass between two probability distributions. Current research focuses on developing efficient algorithms to compute Kantorovich potentials, particularly in high-dimensional spaces, often leveraging neural networks for approximation and employing them in applications like image processing and generative modeling. These advancements are improving the accuracy and scalability of optimal transport methods, impacting fields ranging from machine learning (e.g., Wasserstein GANs) to the numerical solution of complex geometric problems (e.g., finding Calabi-Yau metrics). The ability to efficiently compute these potentials is crucial for advancing these diverse applications.