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