Seminar abstracts: SoSe 2025
Generative AI for the Statistical Computation of Fluids
Samuel Lanthaler, 31.03.2025
In recent years, there has been growing interest in applying neural networks to the data-driven approximation of partial differential equations (PDEs). This talk will discuss a generative AI approach for fast, accurate, and robust statistical computation of three-dimensional turbulent fluid flows. On a set of challenging fluid flows, this approach provides an accurate approximation of relevant statistical quantities of interest while also efficiently generating high-quality realistic samples of turbulent fluid flows. This stands in stark contrast to ensemble forecasts from deterministic machine learning models, which are observed to fail on these challenging tasks. This talk will highlight theoretical results that reveal the underlying mechanisms by which generative AI models can succeed in capturing key physical properties where deterministic ML approaches fall short.
In recent years, there has been growing interest in applying neural networks to the data-driven approximation of partial differential equations (PDEs). This talk will discuss a generative AI approach for fast, accurate, and robust statistical computation of three-dimensional turbulent fluid flows. On a set of challenging fluid flows, this approach provides an accurate approximation of relevant statistical quantities of interest while also efficiently generating high-quality realistic samples of turbulent fluid flows. This stands in stark contrast to ensemble forecasts from deterministic machine learning models, which are observed to fail on these challenging tasks. This talk will highlight theoretical results that reveal the underlying mechanisms by which generative AI models can succeed in capturing key physical properties where deterministic ML approaches fall short.