Solving the Pulsar Equation using Physics-Informed Neural Networks

TL;DR

This paper demonstrates the use of Physics-Informed Neural Networks to model pulsar magnetospheres, successfully reproducing known models and highlighting PINNs as a promising tool for complex astrophysical PDE problems.

Contribution

The study introduces a PINN-based approach for solving pulsar magnetospheric PDEs, enabling accurate modeling of axisymmetric configurations and current sheet features.

Findings

Reproduced various axisymmetric pulsar models from literature.

Energy loss estimates are within a factor of three of classical dipole models.

PINNs show potential for 3D magnetosphere modeling.

Abstract

In this study, Physics-Informed Neural Networks (PINNs) are skilfully applied to explore a diverse range of pulsar magneto-spheric models, specifically focusing on axisymmetric cases. The study successfully reproduced various axisymmetric models found in the literature, including those with non-dipolar configurations, while effectively characterizing current sheet features. Energy losses in all studied models were found to exhibit reasonable similarity, differing by no more than a factor of three from the classical dipole case. This research lays the groundwork for a reliable elliptic Partial Differential Equation solver tailored for astrophysical problems. Based on these findings, we foresee that the utilization of PINNs will become the most efficient approach in modelling three-dimensional magnetospheres. This methodology shows significant potential and facilitates an effortless generalization, contributing to the advancement of our understanding of pulsar magnetospheres.