Optimal Coupling

Optimal coupling, a core concept in probability and optimization, seeks to find the most efficient way to match elements from two probability distributions, minimizing a specified cost function. Current research focuses on developing efficient algorithms for optimal coupling in various contexts, including domain decomposition methods for coupling reduced-order models of partial differential equations and neural network-based approaches for unbalanced optimal transport. These advancements are impacting diverse fields, from accelerating Monte Carlo simulations and improving large language model decoding to enhancing the accuracy of physics-informed neural networks for solving complex equations and enabling novel applications in computer vision and single-cell biology.