Using Machine Learning Based Moment Closures to Capture Kinetic Turbulence*

Gyrofluid models are attractive because they provide a computationally efficient alternative to gyrokinetic models. They rely on a moment closure, which approximates the highest order fluid moment as a function of the lower order moments. Conventional gyrofluid models use linear moment closures designed to match the plasma dispersion function and can produce linear physics that closely matches gyrokinetics in many parameter regimes. However, these linear closures can break down in the presence of turbulence, where the nonlinearity can strongly modify the kinetic physics. We apply a machine learning approach to developing moment closures that correctly capture kinetic effects in a relatively simple kinetic turbulent system produced by the DNA code. The DNA code solves a set of reduced gyrokinetic equations in a Hermite representation, which lends itself naturally to a moment closure. The algorithms are trained on kinetic simulation data (i.e. using dozens of Hermite moments) and are designed to predict a closure for a four moment system of equations.