发表机构
Universitat de les Illes Balears; Institute of Applied Computing & Community Code (IAC3); Universitat d’Alacant; Facultad de Matemática, Astronomía, Física y Computación, Universidad Nacional de Córdoba; Instituto de Física Enrique Gaviola, CONICET（巴利阿里群岛大学; 应用计算与社区代码研究所; 阿利坎特大学; 科尔多瓦国立大学数学、天文学、物理和计算机学院; 恩里克·加维亚多物理研究所，阿根廷国家科学和技术研究委员会）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究物理信息神经网络在广义相对论中的应用，通过数值相对论基准和孤立玻色子星演化验证其能准确求解爱因斯坦方程，确立其作为求解耦合物质-爱因斯坦方程的补充框架。
AI 中文摘要
物理信息神经网络（PINNs）是一种机器学习框架，通过约束神经网络满足底层物理定律来逼近偏微分方程组的解。由此产生的连续表示不需要预定义的计算网格，并且可以在训练域内的任意点进行评估。在这项工作中，我们研究了将PINNs应用于爱因斯坦广义相对论方程的问题。我们讨论了用于获得精确时空解的数学公式、网络架构、损失函数和训练策略，并通过一系列数值相对论的标准基准来演示该方法。然后，我们将该方法扩展到更具天体物理学背景的场景，考虑孤立孤子玻色子星的动力学演化。我们的模拟表明，直接在三维笛卡尔坐标中运行的PINN可以重现高度致密玻色子星的平衡结构，并恢复其特征径向振荡频率。这些结果确立了PINNs作为求解耦合物质-爱因斯坦方程和探索数值相对论中替代公式的可行补充框架。
英文摘要
Physics-Informed Neural Networks (PINNs) are a machine-learning framework for approximating solutions to systems of partial differential equations by constraining neural networks to satisfy the underlying physical laws. The resulting continuous representation does not require a predefined computational mesh and can be evaluated at arbitrary points within the training domain. In this work, we investigate the application of PINNs to Einstein's equations of General Relativity. We discuss the mathematical formulation, network architectures, loss functions, and training strategies used to obtain accurate spacetime solutions, and demonstrate the approach through a series of standard benchmarks from Numerical Relativity. We then extend the method to a more astrophysical setting by considering the dynamical evolution of an isolated solitonic boson star. Our simulations show that a PINN operating directly in three-dimensional Cartesian coordinates can reproduce the equilibrium structure of a highly compact boson star and recover its characteristic radial oscillation frequencies. These results establish PINNs as a viable complementary framework for solving coupled matter-Einstein equations and exploring alternative formulations in numerical relativity.
