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


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.