A New Model of the Crustal Magnetic Field of Mars Using Physics-Informed Neural Networks

Mars possesses a strong remanent crustal field, indicative of an ancient magnetic dynamo which is now inactive. We address the problem of modelling this field using magnetometer measurements from two orbiters, MGS (1997 – 2006) and MAVEN (since 2014).

A substantial amount of additional low-altitude data has been collected by MAVEN since the most recent and highest resolution global model was published, thereby necessitating a new model to be computed. Two approaches were formally used for this: Spherical Harmonics (SH) and Equivalent Source Dipoles (ESD). We propose to solve this regression problem with an ensemble of Physics-Informed Neural Networks (PINN). With this approach, (1) the generalization performance of our model is monitored while relying solely on the data for this purpose; (2) the entire datasets are used without the need to down-sample; (3) the resolution varies with respect to the nonuniform data coverage; and (4) model uncertainty is estimated.

The input of each network is the observer coordinates in the Mars body-fixed reference frame, and the output is a scalar potential. The predicted magnetic field is computed from this scalar potential with automatic differentiation before updating the free parameters with back-propagation. As such, the conservative nature of the magnetic field is encoded as a hard constraint. The estimation of prediction uncertainties relies on an implicit regularization scheme based on bootstrap aggregating and early stopping. From predicted values of the magnetic field and corresponding variances, a spherical harmonics expansion was performed with a weighted least-squares.

The corresponding spherical harmonics degree spectrum at orbit altitude is stable up to degree 160 and has more energy than previous models. The improved resolution of this model opens doors for future research and has potential for scientific inferences regarding the crustal magnetism of Mars and its interactions with the induced magnetosphere.