AI 中文总结
该研究开发物理信息神经网络（PINN），直接学习玻色星平衡解流形上的场映射，可单次生成完整构型，成功重构多分支玻色星族的关键特征，为非线性自引力解族探索提供实用方法。
AI 中文摘要
传统计算玻色星族需要反复求解非线性特征值边值问题，并通过转折点进行精细的数值延拓。我们开发了一种物理信息神经网络（PINN），它直接学习从物理参数和径向坐标到平衡解流形上标量场和度规场的映射。网络输出中融入了正则性和渐近边界条件，训练目标结合了逐点监督、爱因斯坦-克莱因-戈登残差以及对阿诺维特-德塞-米斯纳质量和诺特定理电荷的曲线级约束。训练好的模型可通过单次前向传播生成完整构型。在代表性的单分支、双分支和三分支族中，该方法重构了质量-频率螺旋结构和守恒量，包括传统求解器中需要精细延拓的内分支构型。这些结果表明，物理信息代理学习是探索非线性自引力解族的实用摊销途径。
英文摘要
Computing boson star families traditionally requires repeated solution of nonlinear eigenvalue boundary-value problems and careful numerical continuation through turning points. We develop a physics-informed neural network (PINN) that learns the map from the physical parameters and radial coordinate directly to the scalar and metric fields over an equilibrium solution manifold. Regularity and asymptotic boundary conditions are incorporated into the network output, while the training objective combines pointwise supervision, Einstein-Klein-Gordon residuals, and curve-level constraints on the Arnowitt-Deser-Misner mass and Noether charge. A trained model generates a complete configuration in a single forward pass. Across representative one-, two-, and three-branch families, the method reconstructs the mass-frequency spirals and conserved quantities, including configurations on inner branches that require delicate continuation in conventional solvers. These results establish physics-informed surrogate learning as a practical route to amortized exploration of nonlinear self-gravitating solution families.
Comments9 pages, 5 figures
