Manifold learning to detect the transition from kinetics to hydrodynamics

In certain regimes, hydrodynamic models provide reduced descriptions of kinetic models. These reduced models are expected to be accurate when the dynamics are sufficiently near collisional equilibrium. Precise characterization of this ``nearness'' has been an active area of research, appearing for instance in David Hilbert's influential list of open mathematical problems posed at the beginning of the 20th century. In this work, we use manifold learning to identify transitions from the kinetic regime to the hydrodynamic regime. To employ manifold learning in this context, an ensemble of initial conditions is evolved using a BGK kinetic equation. As collisions increase entropy, the ensemble of initial conditions collapses onto a space of reduced dimensionality --- one that could in principle be parameterized by hydrodynamic fields. Manifold learning provides a novel means of characterizing this reduced dimensionality and therefore informing the realm of validity of hydrodynamic approximations. We will demonstrate the technique in representative problems and discuss sensitivity with respect to variations in the study parameters. LLNL-ABS-753699