Generative AI for the statistical computation of fluids

Data Science Seminar

Samuel Lanthaler (Caltech)

Abstract

Neural networks have proven to be effective approximators of high dimensional functions in a wide variety of applications. In scientific computing, high-dimensional functions often arise as discretizations of an underlying PDE solution operator. In recent years, there has been growing interest in the use of neural networks for the data-driven approximation of such operators. This talk will focus on a recent application of such data-driven methodology to the statistical computation of fluid flows. In this application, the choice of training objective is observed to lead to stark differences in the empirically achieved results. It will be argued that implicit constraints, related to potential limitations of what is practically achievable by deep learning, could provide a theoretical explanation of these observations.