Data-driven state and parameter estimation for low temperature plasmas

While physics-based models help advance the understanding of complex phenomena in low-temperature plasmas, data-driven models are emerging as promising alternatives. This is due to the increasing availability of data enabled by advances in diagnostic techniques, novel numerical algorithms, improved computational tools, and expanding computing resources. Data assimilation (DA) is a modeling framework that combines the estimation obtained from physics-based models and noisy experimental data to infer, predict, and control the states and parameters of a dynamical system. DA has been successfully used for a wide range of applications, including weather forecasting, robotics, and guidance, navigation, and control. In this talk, we will present the development of data-driven estimation techniques for gas dynamics and low temperature plasmas. In particular, we will discuss the development of various Kalman filters, such as the extended and ensemble Kalman filters (EKF/EnKF), which involve a two-step process: (i) predict the evolution of the state variables using a dynamical physics-based model and (ii) correct the prediction with observation/measurement data. The correction process is determined by the probability density function of the estimated state variables and parameters as well as the measurement uncertainties. We have demonstrated state and parameter estimation for low temperature plasmas 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, extrapolation of plasma-based propulsion performance to in-space conditions, and estimation of electron energy distribution function using optical emission spectroscopy. In addition, we will present the DA framework for partial differential equations (PDEs) to infer the spatio-temporal profile of parameters within the PDEs.