Neural Network Reconstruction of Plasma Space-Time

We explore the use of Physics-Informed Neural Networks (PINNs) for reconstructing full magnetohydrodynamic solutions from partial samples, mimicking the recreation of space-time environments around spacecraft observations. We use one-dimensional magneto- and hydrodynamic benchmarks, namely the Sod, Ryu-Jones, and Brio-Wu shock tubes, to obtain the plasma state variables along linear trajectories in space-time. These simulated spacecraft measurements are used as constraining boundary data for a PINN which incorporates the full set of one-dimensional (magneto) hydrodynamics equations in its loss function. We find that the PINN is able to reconstruct the full 1D solution of these shock tubes even in the presence of Gaussian noise. However, our chosen PINN transformer architecture does not appear to scale well to higher dimensions. Nonetheless, PINNs in general could turn out to be a promising mechanism for reconstructing simple magnetic structures and dynamics from satellite observations in geospace.