A Learned Fluid Closure for Phase Mixing Applied to a Turbulent Gradient-Driven Gyrokinetic System in Simple Geometry*

We present a new method for formulating closures that learn from kinetic simulation data. We apply this method to phase mixing in a simple gyrokinetic turbulent system - temperature gradient driven turbulence in an unsheared slab. The closure is motivated by the observation that in a turbulent system the nonlinearity continually perturbs the system away from the linear solution, thus demanding versatility in the closure scheme. The closure, called the learned multi-mode (LMM) closure, is constructed by, first, extracting an optimal basis from a nonlinear kinetic simulation using singular value decomposition (SVD). Subsequent nonlinear fluid simulations are projected onto this basis and the results are used to formulate the closure. We compare the closure with several other closures schemes over a broad range of the relevant 2D parameter space (collisionality and gradient drive). We find that the turbulent kinetic system produces phase mixing rates much lower than the linear expectations. In contrast with the other closures, the LMM closure is able to capture this reduction. In comparisons of heat fluxes, the LMM closure exhibits errors substantially lower than the other closures.