Shallow Recurrent Decoder for Reduced Order Modeling of Plasma Dynamics

Reduced order models are becoming increasingly important for rendering complex and multiscale spatio-temporal dynamics computationally tractable. The computational efficiency of such surrogate models is especially important for design, exhaustive exploration and physical understanding. Plasma simulations, in particular those applied to the study of ${\bf E}\times {\bf B}$ plasma discharges and technologies, such as Hall thrusters, require substantial computational resources in order to resolve the multidimentional dynamics that span across wide spatial and temporal scales. Although high-fidelity computational tools are available to simulate such systems over limited conditions and in highly simplified geometries, simulations of full-size systems and/or extensive parametric studies over many geometric configurations and under different physical conditions are computationally intractable with conventional numerical tools. Thus, scientific studies and industrially oriented modeling of plasma systems, including the important ${\bf E}\times {\bf B}$ technologies, stand to significantly benefit from reduced order modeling algorithms. We develop a model reduction scheme based upon a {\em Shallow REcurrent Decoder} (SHRED) architecture. The scheme uses a neural network for encoding limited sensor measurements in time (sequence-to-sequence encoding) to full state-space reconstructions via a decoder network. Based upon the theory of separation of variables, the SHRED architecture is capable of (i) reconstructing full spatio-temporal fields with as little as three point sensors, even the fields that are not measured with sensor feeds but that are in dynamic coupling with the measured field, and (ii) forecasting the future state of the system using neural network roll-outs from the trained time encoding model.