State and parameter estimation using data assimilation for plasma dynamics and chemistry

Data assimilation (DA) addresses the challenge of reconciling physics-based models with noisy experimental data to estimate the states and parameters of a system. In this talk, I will present the development of DA techniques tailored for plasma dynamics and chemistry using variants of Kalman filters, such as the extended and ensemble Kalman filters (EKF/EnKF), which have been widely used in a range of applications including weather forecasting, control engineering, and robotics. The basic idea of Kalman filters involves a two-step process: (i) predict the evolution of the state variables using a dynamical model and (ii) correct the prediction with observed data. The correction using the data is determined by the first and second moments of the probability density function, i.e., mean and covariance, associated with the estimated state variables and parameters as well as the uncertainties inherent in both the model and the measurements. State and parameter estimation is demonstrated using various zero-dimensional (0D) plasma models, including the predator-prey model of ionization oscillations in partially magnetized plasmas, plasma chemistry in pulsed inductively coupled plasmas, anomalous electron transport in cross-field discharges, and extrapolation of plasma-based propulsion performance to in-space conditions. Furthermore, I will discuss our recent development of EKF and EnKF for 1D partial differential equations (PDEs) to infer the spatio-temporal profile of parameters within the PDEs. The proposed approach enables robust estimation of state variables and parameters even only when temporally and spatially sparse data are available.