Abstract
Generative models based on dynamic transport have recently led to significant advances in unsupervised learning. Mathematically, these models are primarily built around the construction of a function between two probability distributions that transforms samples from the first into samples from the second. Although these methods were initially introduced in the context of image generation, they have found a wide range of applications, particularly in scientific computing, where they offer interesting ways to rethink complex problems once considered unsolvable due to the curse of dimensionality.
In this presentation, we will discuss the mathematical foundations of generative models based on flows and diffusions, and show how a better understanding of their inner workings can help improve their design. These results indicate how to structure transport to best achieve complex target distributions while maintaining computational efficiency, both during the training and sampling stages.
We will also discuss applications of generative AI in scientific computing, particularly in the context of Monte Carlo sampling, with applications to statistical mechanics and Bayesian inference, as well as probabilistic forecasting, with applications to fluid dynamics and atmospheric and ocean sciences.
