Dimension reduction in physical and data sciences

Reduction and Inflation of Linear Models with an Application to Moment Closures of the Linearized Boltzmann Equation

C. Dave Levermore

University of Maryland
[SLIDES]

Model reduction builds a smaller model from a larger one. Model inflation is a learning algorithm that builds a larger model from a smaller one within the framework of a family of models. We present a framework for model reduction of linear models that have a dissipative structure and give conditions under which the structure is preserved. We apply this framework to build a family of well-posed moment closures for the linearized Boltzmann equation. For a given choice of moments we present their Galerkin, semi-relaxation, and first-correction closures and show the relationship of these three closures to the linearized Euler, Navier-Stokes, and Burnett systems of gas dynamics.