Hydrodynamic Models: Machine Learning for Kinetic Equations

This lecture explores the development of uniformly accurate hydrodynamic models for kinetic equations using machine learning. Starting with the Boltzmann equation, the instructor discusses numerical challenges, the fluid dynamical description, and the general strategy for modeling multi-scale physics. The lecture delves into moment methods, machine-learned moment methods, and the learning of moment fluxes and source terms. It also covers Galilean invariant moments, numerical results of various tasks, and end-to-end learning strategies in detail.