Shallow recurrent decoder for reduced order modeling of <i>E</i> × <i>B</i> plasma dynamics

Abstract Reduced-order models (ROMs) are becoming increasingly important for rendering complex and multiscale spatiotemporal dynamics computationally tractable. Computationally efficient ROMs are especially essential for optimized design of technologies as well as for gaining physical understanding. Plasma simulations, in particular those applied to the study of E × B plasma discharges and technologies, such as Hall thrusters for spacecraft propulsion, require substantial computational resources in order to resolve the multidimensional dynamics that span across wide spatial and temporal scales. While high-fidelity computational tools are available, their applications are limited to simplified geometries and narrow conditions, making simulations of full-scale plasma systems or comprehensive parametric studies computationally prohibitive. In addition, experimental setups involve limitations such as the finite spatial resolution of diagnostics and constraints imposed by geometrical accessibility. Consequently, both scientific research and industrial development of plasma systems, including E × B technologies, can greatly benefit from advanced ROM techniques that enable estimating the distributions of plasma properties across the entire system. We develop a model reduction scheme based upon a shallow recurrent decoder (SHRED) architecture using as few measurements of the system as possible. This scheme employs a neural network to encode limited sensor measurements in time (of either local or global properties) and reconstruct full spatial state vector via a shallow decoder network. Leveraging the theory of separation of variables, the SHRED architecture demonstrates the ability to reconstruct complete spatial fields with as few as three-point sensors, including fields dynamically coupled to the measured variables but not directly observed. The effectiveness of the ROMs derived with SHRED is demonstrated across several plasma configurations representative of different geometries in typical E × B plasma discharges and Hall thrusters.