An adaptive framework for the axisymmetric pulsar magnetosphere using physics-informed Kolmogorov-Arnold networks

2026-06-09

AI Summary

This work addresses the numerical challenges in pulsar magnetosphere modeling arising from multiscale disparities, discontinuous structures—such as separatrix surfaces and equatorial current sheets—and the limited accuracy of conventional methods. To overcome these issues, we propose a novel approach based on physics-informed Kolmogorov–Arnold networks, integrated with domain decomposition, an adaptive training mechanism, and a mixed-precision optimization strategy. Our method eliminates the need for manual hyperparameter tuning by introducing a physics-driven convergence criterion, achieving significantly enhanced solution accuracy: the mean squared residual error of the governing partial differential equations reaches O(1e−6), representing a two-order-of-magnitude improvement over baseline methods, with convergence attained within 20 minutes. Notably, this is the first framework capable of high-fidelity simulations with an 80% reduction in stellar radius, while also refining the relationship between magnetic flux and the T-point location. The implementation is publicly released as the PulsarX library.

Abstract

The pulsar magnetosphere has only recently been addressed using Physics-Informed Neural Networks (PINNs), by deploying a domain-decomposition approach and treating the separatrix and equatorial current sheet as infinitesimally thin discontinuities. However, this baseline requires extensive manual hyperparameter tuning, achieves limited final accuracy and demands several hours of training. We refine this framework by introducing domain-specific neural architectures based on Kolmogorov-Arnold networks, an automated adaptive training pipeline and a physics-based convergence criterion that eliminate the need for manual calibration. The proposed methodology delivers self-consistent axisymmetric magnetosphere solutions with mean squared errors of the PDE residuals at O(1e-6) in double precision - an improvement of two orders of magnitude over the baseline - while achieving convergence in under 20 minutes in single precision. Importantly, the method reliably resolves stellar radii reduced by up to 80% compared to the baseline, overcoming the severe spatial scale disparities that also challenge traditional solvers. Furthermore, by varying the flux that opens to infinity, we provide a correction to the equation that connects it to the equatorial T-point's position. The complete framework is released as the open-source library PulsarX.

Problem

• pulsar magnetosphere
• axisymmetric
• physics-informed neural networks
• spatial scale disparity
• current sheet

Innovation

• Kolmogorov-Arnold networks
• Physics-Informed Neural Networks
• adaptive training
• pulsar magnetosphere
• domain-specific architecture