Phenomenological modeling of plasma transport via stochastic filtering

The accuracy of first-principles predictive models for the evolution of plasma profiles is sometimes limited by the lack of understanding of the plasma transport phenomena. It is possible then to develop approximate transport models for the prediction of the plasma dynamics which are consistent with the available diagnostic data. This data-driven approach, usually referred to as phenomenological modeling, arises as an alternative to the more classical theory-driven approach. In this work we propose a stochastic filtering approach based on an extended Kalman filter to provide real-time estimates of poorly known or totally unknown transport coefficients. We first assume that plasma dynamics can be governed by tractable models obtained by first principles. However, the transport parameters are considered unknown and to-be-estimated. These estimates will be based solely on input-output diagnostic data and limited understanding of the transport physics. Numerical methods (e.g., finite differences) can be used to discretize the PDE models both in space and time to obtain finite-dimensional discrete-time state-space representations. The system states and to-be-estimated parameters are then combined into an augmented state vector. The resulting nonlinear state-space model is used for the design of an extended Kalman filter that provides real-time estimations not only of the system states but also of the unknown transport coefficients. Simulation results demonstrate the effectiveness of the proposed method for a benchmark transport model in cylindrical coordinates.