Data driven construction of MHD surrogates using sparse regression and data assimilation

Tokamak operation is plagued by the presence of magnetohydrodyamic instabilities which impose limitations on their efficiency and can cause early termination of the plasma. Understanding of many of these instabilities comes from nonlinear numerical simulations of resistive magnetohydrodynamics which are challenging to perform owing partly to the timescales that must be resolved. Fortunately, simplified ordinary differential equations called the ANAC and ANAET models can be derived using symmetry arguments with bifurcation theory which display qualitative similarities to observed tokamak instabilities. The qualitative similarity of these models motivates exploring approaches which allow them to be related quantitatively to experiment.

In this dissertation we implement two data-driven approaches which can be used to either derive simplified models of tokamak instabilities or be used to match already known simplified models to experimental diagnostics. The first of these methods is a popular regression framework called the sparse identification of nonlinear which we validate on a low-dimensional model of magnetoconvection behaviour and use to derive low-dimensional models directly from numerically simulated magnetoconvection PDE data. We suggest that implementation of the weak form and constraints are almost certainly required in future applications. Results show that models derived from POD modes of magnetoconvection PDE data can show expected bifurcations present in the PDE.

The second approach is called the ensemble Kalman filter and is applied to two models which resemble the sawtooth instability in tokamaks. We demonstrate how the ensemble Kalman filter can be used for parameter estimation of these two models in experiment like conditions, displaying robustness to high degrees of noise, low sampling rates and multiscale dynamics. By using a stochastic integration scheme, we draw parallels between observed sawtooth instabilities in tokamaks and the ANAET model.