Abstract
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.
Highlights
Machine learning techniques for space science have grown popular in recent years, with diverse applications across the coupled Sun-Earth system
We explore the use of Physics-Informed Neural Networks (PINNs) for reconstructing information from simulated spacecraft measurements within one-dimensional hydrodynamic (HD) and magnetohydrodynamic (MHD) benchmark problems
We find that the Brio-Wu shock tube is a more difficult reconstruction, especially in the shock region
Summary
Machine learning techniques for space science have grown popular in recent years, with diverse applications across the coupled Sun-Earth system These include coronal holes (Bloch et al, 2020; Illarionov et al, 2020), solar flare forecasting (Li X. et al, 2020; Wang X. et al, 2020), solar wind prediction (Upendran et al, 2020), and space weather forecasting (Camporeale (2019) and references), among other applications. If we wish to provide global context, we use large-scale, computationallyintensive global magnetohydrodyamic simulations of the magnetosphere (e.g., SWMF (Tóth et al, 2005), GAMERA (Zhang et al, 2019), OpenGCCM (Raeder et al, 2001), Gkeyll (Dong et al, 2019)) These simulations are typically initialized with solar wind conditions closest to the time of interest, and compared directly with the spacecraft observations after run completion. It is often too computationally expensive to run multiple iterations in order to best fit the data, especially for more advanced simulations which extend beyond ideal MHD
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