Spatiotemporal forecasting of plasma turbulence

In recent years, we have seen a growing interest in the use of machine learning models for fusion plasmas, be it disruption mitigation, fluid closures or turbulence forecasting. Some of these tools can provide us with key insights into phenomena that might otherwise remain concealed when using traditional numerical codes. To that end, we use a deep learning model called a Convolutional Gated Recurrent Unit (ConvGRU) to forecast spatiotemporal turbulence. We obtain the data by solving a reduced electrostatic turbulence model for the Ion Temperature Gradient turbulence~\cite{ivanov2020zonally} using the GX~\cite{mandell2018laguerre} code and train our deep learning model to predict non-zonal temperature, $E \times B$ flow fluctuations and the resulting heat flux Q. We show that the time-averaged flux predicted by the ConvGRU matches well with the heat flux from the ground truth.

One major advantage of these deep learning networks is the ability to calculate the Lyapunov exponents of a dynamical system. Haller et al.~\cite{haller2015lagrangian} have shown in the past that the Lyapunov exponents are directly related to the Cauchy-Green strain tensor. We believe that the Lyapunov exponents might yield information about the relative effects of two competing stresses in Ivanov's edge turbulence model: the Reynolds stress and $E \times B$ diamagnetic stress. To that end, we calculate the Lyapunov spectrum of the simulation data and find correlations between the heat flux and the max Lyapunov exponent.