The Pulsar Magnetosphere with Machine Learning: Methodology

Ioannis Contopoulos, Ioannis Dimitropoulos, Vassilis Mpisketzis, Evangelos Chaniadakis

Published 2023-09-13Version 1

We propose a new method for obtaining the general solution of the ideal force-free steady-state pulsar magnetosphere in 3D. We divide the magnetosphere in the regions of closed and open field lines and train two custom Physics Informed Neural Networks (PINNs) to yield the solution in each of these two regions. We also periodically adjust the shape of the separatrix between the two regions to satisfy pressure balance everywhere. Our method introduces several innovations over traditional methods that are based on numerical grids and finite differences. In particular, it introduces a proper treatment of mathematical contact discontinuities in FFE. We present preliminary results in axisymmetry which confirm the significant potential of our method.