Young Researchers Workshop: Kinetic models in biology and social sciences

Detecting the transition from kinetics to hydrodynamics using manifold learning

Lee Ellison

Lawrence Livermore National Laboratory

During the kinetic evolution of a gas or plasma, collisional events increase entropy and drive the system toward collisional equilibrium. The Bogoliubov hypothesis posits that on timescales long relative to the collision time, the dynamics may be well described by a reduced, hydrodynamic description. Analytically, it can be difficult to describe this transition; existence and identification of a slow, invariant hydrodynamic manifold has only been rigorously established for limiting cases and/or simplified kinetic descriptions. In this work, we supplement analytic analysis this transition with statistical analyses of numerical datasets. We perform ensembles of kinetic simulations to evolve a high-dimensional volume of initial conditions. We then apply manifold learning to search for low-dimensional representations of the data during late stages (i.e., after many collision periods) of evolution. The identification of low-dimensional structure within the dataset indicates a reduced description of the dynamics, such as a hydrodynamic description, is in principle possible. We demonstrate the utility of this analysis in several representative cases of interest. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344, LLNL-ABS-744951