This is a past event.
Title: Structure-Preserving Moment Models for the Radiative Transport and Free Surface Flows
Abstract: The computational cost of solving high-dimensional mathematical models in physics and engineering often poses a significant challenge. This talk focuses on strategies for reducing model complexity while preserving essential mathematical structures, offering a pathway to more efficient and accurate numerical solutions. In the first part, we introduce our machine learning-based approach for constructing moment models tailored for radiative transport equations. Through carefully designed neural network architectures, we ensure the stability (or hyperbolicity) of these moment models. Additionally, we delve into other critical mathematical attributes, such as physical characteristic speeds. In the second half of the talk, we shift our focus to the incompressible Navier-Stokes equations with free surfaces. We explore a novel class of models that describe this system, traditionally modeled using shallow water equations. We demonstrate the rotational invariance and hyperbolicity of these newly-derived shallow water moment models.