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Machine learning of plasma fluid closures, the physics background

Motivation

  • Roughly speaking, there are two major types of plasma simulation codes, kinetic and fluid-based.
    • Kinetic models: track motion of many many particles;
      • Keep (almost) all physics; computationally expensive: example: Particle-in-cell
    • Fluid models: solve PDEs for density, velocity, temperature, etc.;
      • Simplify/Lose certain physics; computationally fast; example: MHD
  • However, a fluid model inevitably makes certain assumptions, or “closures”.
    • Sometimes, a prescribed closure may give inaccurate results for certain problems.
  • Our ultimate goald is to use Machine Learning to extract the more accurate closures from kinetic simulation results.
  • Our goal for this Hackweek is a little bit shifted to make the tasks feasible within the time frame.
    • We will use data computed from a known closure, that works well for a certain type of problems (i.e., 1d electrostatic Landau damping).
    • This work is a reproduction of the work in a recent Ma+ 2020 POP.
    • It is highly likely that the same methodology/enhancement will be usable to train data from actual kinetic simulations.
  • If successful in the end, we could greatly enhance the physics capabilities of existing fluid-based plasma models that are widely used in astrophysics, space physics, laboratory plasma physics.

More on the physics

  • As an example, one could evolve a 1d electrostatic plasma using the following fluid equations



    where t is time, ρ is density, u is velocity, p is pressure, q is heat flux, E is electric field computed/supplied elsewhere, and m is single particle mass.
  • The so-called closure problem here is that we need to specify q which is needed to solve the equations in time.
  • In this project, we consider the closure suggested by (Hammett & Perkins 1990 PRL), which is forumulated in the Fourier space (k-space):

    where is the heat flux fluctuation in the k space is the temperature fluctuation in the k space, is a chosen constant, n0 is the background density, T0 is vt is the background temperature, and is the thermal speed.
  • This closure works well for a certain type of problems (i.e., 1d electrostatic Landau damping). There are other closures that work better for other problems.
  • There are 2d and 3d versions of such closures that we will also explore if time allows.