相对论流体力学中守恒到本原的机器学习
Machine Learning for Conservative-to-Primitive in Relativistic Hydrodynamics
摘要：
守恒型相对论流体力学方程的数值解需要求根算法，将守恒变量映射反演为原始变量映射。这些算法采用流体的状态方程，并且对于涉及复杂的微观物理模型的应用，例如在二元中子星的数值相对论模拟中计算精确的引力波信号所需的那些，在计算上要求很高。这项工作探讨了使用机器学习方法来加快恢复相对论流体动力学中的原语。人工神经网络的训练，以取代一个列表状态方程的插值或直接保守到原始的地图。这些神经网络简单的基准问题的应用表明，这两种方法改善了传统的根查找表状态方程和多维插值。特别是，保守到原始映射的神经网络在保持准确性的同时，比标准方法加速了一个数量级以上的变量恢复。因此，神经网络是一个有趣的选择，以提高相对论流体力学算法的速度和鲁棒性。
英文摘要：
The numerical solution of relativistic hydrodynamics equations in conservative form requires root-finding algorithms that invert the conservative-to-primitive variables map. These algorithms employ the equation of state of the fluid and can be computationally demanding for applications involving sophisticated microphysics models, such as those required to calculate accurate gravitational wave signals in numerical relativity simulations of binary neutron stars. This work explores the use of machine learning methods to speed up the recovery of primitives in relativistic hydrodynamics. Artificial neural networks are trained to replace either the interpolations of a tabulated equation of state or directly the conservative-to-primitive map. The application of these neural networks to simple benchmark problems shows that both approaches improve over traditional root finders with tabular equation-of-state and multi-dimensional interpolations. In particular, the neural networks for the conservative-to-primitive map accelerate the variable recovery by more than an order of magnitude over standard methods while maintaining accuracy. Neural networks are thus an interesting option to improve the speed and robustness of relativistic hydrodynamics algorithms.
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