Physics-informed neural networks (PINNs) for satellite trajectory-based reconstruction: Applications to Grad–Shafranov and magneto-hydrostatic equilibria

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Abstract
This study demonstrates the effectiveness of physics-informed neural networks (PINNs) for reconstructing Grad–Shafranov (GS) equilibrium structures from synthetic, noise-free trajectory-like data representative of satellite measurements under both GS and magnetohydrostatic constraints. The proposed framework focuses on inferring continuous two-dimensional equilibrium structures from limited and sparsely sampled measurements along trajectories analogous to satellite sampling using static equilibrium solutions without explicitly provided boundary conditions. The sinusoidal representation network-enhanced architecture played a key role in capturing fine-scale structures. By incorporating uncertainty weighting, the model ensured balanced optimization, leading to higher accuracy and more effective enforcement of physical constraints. Additionally, the study highlights the importance of diverse training data, including multi-component measurements and data from multiple trajectories. The integration of such data significantly improved model performance by reducing errors and uncertainty while stabilizing training dynamics. These findings suggest that, even in the absence of explicit boundary conditions, which are commonly incorporated in PINN research, multi-component and multi-trajectory data can provide additional directional information that guides the solution process, reduces reconstruction ambiguity, and improves the reliability of the reconstructed solution.
Funding Information
  • Heliophysics Division (NASA 80NSSC23K0417)
  • Japan Society for the Promotion of Science (KAKENHI 25K07256)

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