Data-driven inference of high-dimensional spatiotemporal state of plasma systems

Abstract

Many plasma systems and technologies, such as Hall thrusters for spacecraft propulsion, exhibit complex underlying physics that affect the global operation. When characterizing such systems in an experiment, obtaining full spatiotemporal maps of the involved state variables can be, thus, highly informative. However, this goal is not practically realizable because of various experimental limitations, e.g., finite spatial resolution of the diagnostics and geometrical accessibility constraints. Therefore, having the capability to reconstruct the full high-dimensional states of plasma systems from low-dimensional time-history measurements is greatly desirable. Compressed sensing is a signal processing technique that can answer this crucial need. However, existing compressed sensing approaches have several limitations that restrict their effectiveness for complex physical systems like plasma technologies. These include the need for abundant sensor measurements and a principled sensor placement. In this paper, we demonstrate the capabilities of Shallow Recurrent Decoder (SHRED) architecture for compressed sensing. We show in several plasma test cases that SHRED can robustly infer full high-dimensional spatiotemporal state vectors of these systems (i.e., all macroscopic plasma properties) from minimal system information. This minimal information can consist of three finite time-history measurements of either local values of a plasma property or the global plasma properties (spatially averaged or performance parameters). An application of SHRED's inference capability in the numerical plasma simulation context is “super-resolution” enhancement. We will discuss this application by presenting how SHRED can effectively establish mappings between a low-resolution and a high-resolution simulation, recovering detailed spatial plasma features that are below the simulation's grid size.