Reconstructions of Jupiter's magnetic field using physics informed neural networks

TL;DR

This study introduces physics-informed neural networks (PINNs) to reconstruct Jupiter's internal magnetic field from Juno data, addressing the noise amplification that plagues inward continuation under zero-conductivity assumptions and spherical-harmonic limits. By representing the field via a vector potential and enforcing physics constraints through a loss that penalizes current density, the method tolerates weak currents and focuses on local structures, improving depth resolution. Four PINN configurations based on different orbital subsets (PINN33i/33e and PINN50i/50e) yield depth-resolved maps that are comparable to, yet clearer than, traditional spherical-harmonic reconstructions, with a dynamo boundary inferred near $r \approx 0.8R_J$. The results demonstrate diminished small-scale noise at depth and reveal longitudinal banding and hemispheric structure, suggesting a more nuanced interior dynamo region and offering a path for secular-variation studies and applications to other planets.

Abstract

Magnetic sounding using data collected from the Juno mission can be used to provide constraints on Jupiter's interior. However, inwards continuation of reconstructions assuming zero electrical conductivity and a representation in spherical harmonics are limited by the enhancement of noise at small scales. Here we describe new reconstructions of Jupiter's internal magnetic field based on physics-informed neural networks and either the first 33 (PINN33) or the first 50 (PINN50) of Juno's orbits. The method can resolve local structures, and allows for weak ambient electrical currents. Our models are not hampered by noise amplification at depth, and offer a much clearer picture of the interior structure. We estimate that the dynamo boundary is at a fractional radius of 0.8. At this depth, the magnetic field is arranged into longitudinal bands, and strong local features such as the great blue spot appear to be rooted in neighbouring structures of oppositely signed flux.

Figures (5)

• Figure 1: Juno data used in this work. Left: Juno's global coverage after 50 orbits, showing Juno's trajectory within radius $2.5~R_J$; the colours show the 33 prime mission orbits (red lines) and the extended mission, orbits 34 onwards (blue lines). Upper right: time span and magnitude range per orbit of Juno magnetic data. Lower right: orbital position (radius within $4.0~R_J$) projected onto a background contour map of the magnitude of magnetic field at $r=R_J$ reconstructed using model PINN50e.
• Figure 2: Orbital comparison of the discrepancy between various reconstructions of Jupiter's magnetic field: PINN33e, PINN50e, JRM33 and Baseline, with the Juno data. On each orbit, the error is quantified by taking the root mean squared value of the vector difference between the reconstructed magnetic field and the Juno measurements, similar to the data-loss term. We show the (upper) absolute value of this error, and (lower) relative value, $E_2$, of this error compared to the rms observed magnitude over the orbit. The dashed line delineates the prime from the extended mission.
• Figure 3: The magnitude of current density $|\bf J|$ from PINN50e and PINN50i shown on illustrative radii $(r/R_J = 0.8, 1, 1.5, 4$) on a Mollweide projection with the central meridian at a longitude of $180^o$ west (System III coordinates).
• Figure 4: The radial component of Jupiter's magnetic field on various spherical radii inside Jupiter's surface. The plots are shown on a Mollweide projection with the central meridian at a longitude of $180^o$ west (System III coordinates). Left column shows the JRM33 model, $N=18$Connerney_etal_2022, the middle column shows the Baseline model, $N=32$Bloxham_etal_2022 and the right column shows the model PINN50i.
• Figure 5: Upper panel: Gauss coefficients of PINN50e at $r=R_J$, JRM33 and Baseline. Middle panel: Lowes-Mauersberger spectrum of three inwards analytically continued models (coloured lines): PINN50e ($N=35$), JRM33 ($N=30$) and Baseline ($N=32$); black symbols show similar spectra obtained from extrapolation using PINN50i in $r<R_J$ (squares: $0.80 R_J$; triangles: $0.85 R_J$). Lower panel: spectral slope (fit to degrees 2--18), with radius for four analytically continuated models: JRM33, Baseline, PINN33e and PINN50e.