AMS Weekly Seminar | Professor Eric Vanden-Eijnden

Location:Gilman 132

When: February 8th at 1:30 p.m.

Title: Scientific Computing in the Age of Generative AI

Abstract: Generative models based on dynamical transport have recently led to significant advances in unsupervised learning. At mathematical level, these models are primarily designed around the construction of a map between two probability distributions that transform samples from the first into samples from the second.  While these methods were first introduced in the context of image generation, they have found a wide range of applications, including in scientific computing where they offer interesting ways to reconsider complex problems once thought intractable because of the curse of dimensionality. In this talk, I will discuss the mathematical underpinning 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 the transport to best reach complex target distributions while maintaining computational efficiency, both at learning and sampling stages.  I will also discuss applications of generative AI in scientific computing, in particular in the context of Monte Carlo sampling, with applications to the statistical mechanics and Bayesian inference, as well as probabilistic forecasting, with application to fluid dynamics and atmosphere/ocean science.

Bio: Eric Vanden-Eijnden ( https://wp.nyu.edu/courantinstituteofmathematicalsciences-eve2/ ) is a Professor of Mathematics at the Courant Institute of Mathematical Sciences, New York University.  His research focuses on the mathematical and computational aspects of statistical mechanics, with applications to complex dynamical systems arising in molecular dynamics,  materials science, atmosphere-ocean science, fluids dynamics, and neural networks. He is also interested in the mathematical foundations of machine learning (ML) and the applications of ML in scientific computing. He is known for the development and analysis of multiscale numerical methods for systems whose dynamics span a wide range of spatio-temporal scales. He is the winner of the Germund Dahlquist Prize and the J.D. Crawford Prize, and a recipient of the Vannevar Bush Faculty Fellowship.  He was a plenary speaker at the 2015 International Congress of Industrial and Applied Mathematics (ICIAM) in Beijing and an invited speaker at the 2022 International Congress of Mathematics (ICM).

Zoom link: https://wse.zoom.us/j/94601022340