Exploring pseudospectral reduced models of plasma dynamics using machine learning*

A dominant paradigm for studying turbulence in fusion plasmas is to simulate microscale dynamics along magnetic field lines using gyrokinetic codes.  Several of these codes, such as GENE, CGYRO, and GX, employ pseudospectral methods, combining the accuracy of spectral methods with the efficiency gained by avoiding convolutions in nonlinear terms in the spectral domain.  One potential avenue to accelerate these codes would be to increase their accuracy when operated at coarse resolution in velocity space and configuration space.  To that end, we are exploring the potential to integrate machine learning models of small-scale dynamics into coarse-resolution simulations.  In velocity space, we have demonstrated that it is possible to use reservoir computing to construct an accurate spectral dynamical closure to the dynamics of linear Landau damping in an unsheared slab.  We also show a similar closure in a circular, z-pinch-like geometry, in the absence of Landau damping.  In configuration space, we are studying turbulence in the Hasegawa-Wakatani system [1].  We discuss stability challenges for learned closure models with respect to the recent results of Frezat et al., in the context of quasi-geostrophic turbulence parameterization [2]. 

[1] A. Hasegawa and M. Wakatani.  Phys. Rev. Lett.  59 (14), 1987. 

[2] H. Frezat, J. Le Sommer, R. Fablet, G. Balarac, and R. Lguensat.  J. Adv. Model. Earth Sys. 14, 2022.