Machine-Learning Closures of the Kinetic Moment Hierarchy in the Context of Landau Damping

A common approach to understanding microscale dynamics in fusion plasmas is to study the time evolution of the kinetic distribution function. Recently, the GyrokinetX (GX) code demonstrated an efficient method of analysis in the gyrokinetic limit [1]. By taking fluid moments of the fundamental equations (integrating the fundamental equations over velocity space with orthonormal basis weights), it is possible to derive a hierarchy of coupled equations with an attractive feature: near-locality in velocity space. We aim to improve the fidelity of low-resolution simulations by integrating a machine learning algorithm into a numerical solver to develop an artificial closure of the moment hierarchy. We demonstrate the successful application of this method to a variation of the canonical problem of Langmuir wave damping in an unsheared slab, studied by Landau [2] and revisited by Hammett and Perkins with analytic closures [3]. The promising results of our method suggest that machine-learned closures of the full moment hierarchy may be possible to achieve. We are also investigating whether we can develop this approach into an interpretable model.



[1] N. R. Mandell, W. Dorland, and M. Landreman. J. Plasma Phys. 84 (2018).

[2] L. Landau. J. Phys. USSR 10 (1946).

[3] G. W. Hammett and F. W. Perkins. Phys. Rev. Lett. 64 (1990).