The Pulsar Magnetosphere with Machine Learning: Methodology

TL;DR

This paper presents a novel machine learning approach using Physics Informed Neural Networks to solve the complex three-dimensional pulsar magnetosphere problem, effectively handling discontinuities and boundary conditions.

Contribution

The study introduces a new PINN-based methodology for modeling the pulsar magnetosphere, including boundary shape modifications for pressure balance, advancing computational techniques in astrophysics.

Findings

Preliminary axisymmetric results demonstrate potential.

Effective handling of contact discontinuities in FFE.

Insights into neural network challenges in astrophysical modeling.

Abstract

In this study, we introduce a novel approach for deriving the solution of the ideal force-free steady-state pulsar magnetosphere in three dimensions. Our method involves partitioning the magnetosphere into the regions of closed and open field lines, and subsequently training two custom Physics Informed Neural Networks (PINNs) to generate the solution within each region. We periodically modify the shape of the boundary separating the two regions (the separatrix) to ensure pressure balance throughout. Our approach provides an effective way to handle mathematical contact discontinuities in Force-Free Electrodynamics (FFE). We present preliminary results in axisymmetry, which underscore the significant potential of our method. Finally, we discuss the challenges and limitations encountered while working with Neural Networks, thus providing valuable insights from our experience.