arXiv:2606.10686physics.comp-phastro-ph.IM2026-06

用自适应神经网络求解脉冲星磁层,精度提升百倍且训练快20分钟。

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

论文配图:An adaptive framework for the axisymmetric pulsar magnetosphere using physics-informed Kolmogorov-Arnold networks
图 1 · 摘自论文原文
  • 基于柯尔莫戈罗夫-阿诺德网络设计专用神经架构
  • 残差误差达1e-6,收敛时间不足20分钟
  • 可处理缩小80%的星体半径,适合高精度磁层模拟

脉冲星磁层最近通过物理信息神经网络(PINNs)建模,采用区域分解方法,并将分界面和赤道电流片视为无限薄不连续。但该基准方法需大量手动调参,精度有限,训练耗时数小时。本文提出改进框架:引入基于柯尔莫戈罗夫-阿诺德网络的领域特定神经架构、自动化自适应训练流程及基于物理的收敛判据,消除人工校准需求。所提方法在双精度下实现均方误差低至1e-6的自洽轴对称磁层解,较基线提升两个数量级;单精度下20分钟内完成收敛。尤为重要的是,该方法能可靠解析星体半径缩小达80%的情况,克服传统求解器面临的严重空间尺度差异问题。此外,通过改变开向无穷远的通量,修正了其与赤道T点位置之间的关联方程。完整框架已开源为PulsarX库。

原文摘要 · Abstract (English)

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.

脉冲星神经网络磁层模拟PINN

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