Using Variable Size Particles in Phase Space: Towards Machine-Assisted Learning of Optimal, Dynamical, Phase-Space Tiling*

We Use the Code SFK (Shape Function Kinetics) as our baseline and test its efficacy and accuracy on nonlinear driven plasma wave simulations. Our aim is to test a set of ideas on variable size particle tiling which match form to function. Mutually incoherent families of particle shapes and sizes are constructed which try and adapt to multiscale behavior by homing in on different features adaptively. We compare various choices of phase space tiling and various selection criteria wherein optimality is based on sparsity promotion. Test particle orbit reconstructions of phase space density are used to evaluate the  relative merits of different heterogeneous tiling choices. The real goal is to learn proper tiling which can then be used in nearby problems with little change, facilitating families of simulations to be far more robust and efficient than following the old paradigm of von Neumann computing starting from scratch each and every time.  Examples from electron plasma waves, Kinetic Electrostatic Electron Nonlinear (KEEN) waves and their pair plasma analogs KEEPN (Positron) waves will be given.