Modeling self-gravitating gas flows is essential to answering many fundamental questions in astrophysics. This spans many topics including planet-forming disks, star-forming clouds, galaxy formation, and the development of large-scale structures in the Universe. However, the nonlinear interaction between gravity and fluid dynamics offers a formidable challenge to solving the resulting time-dependent partial differential equations (PDEs) in three dimensions (3D). By leveraging the universal approximation capabilities of a neural network within a mesh-free framework, physics informed neural networks (PINNs) offer a new way of addressing this challenge. We introduce the gravity-informed neural network (GRINN), a PINN-based code, to simulate 3D self-gravitating hydrodynamic systems. Here, we specifically study gravitational instability and wave propagation in an isothermal gas. Our results match a linear analytic solution to within 1\% in the linear regime and a conventional grid code solution to within 5\% as the disturbance grows into the nonlinear regime. We find that the computation time of the GRINN does not scale with the number of dimensions. This is in contrast to the scaling of the grid-based code for the hydrodynamic and self-gravity calculations as the number of dimensions is increased. Our results show that the GRINN computation time is longer than the grid code in one- and two- dimensional calculations but is an order of magnitude lesser than the grid code in 3D with similar accuracy. Physics-informed neural networks like GRINN thus show promise for advancing our ability to model 3D astrophysical flows.

翻译：对自引力气体流动的建模是回答天体物理学中许多基本问题的关键，涵盖行星形成盘、恒星形成云、星系形成以及宇宙大尺度结构演化等众多领域。然而，引力与流体动力学之间的非线性相互作用，对求解由此产生的三维含时偏微分方程构成了严峻挑战。物理信息神经网络利用神经网络在无网格框架下的通用逼近能力，为解决这一挑战提供了新途径。我们提出引力信息神经网络（GRINN）——一种基于物理信息神经网络的代码，用于模拟三维自引力流体动力学系统。本文重点研究了等温气体中的引力不稳定性与波传播现象。在线性阶段，我们的结果与线性解析解的误差在1%以内；当扰动增长进入非线性阶段时，与传统网格代码解的误差在5%以内。我们发现，GRINN的计算时间不随维度数量增加而扩展，这与网格代码在流体动力学和自引力计算中随维度增加而表现出的缩放特性形成对比。研究结果表明：在一维和二维计算中，GRINN的计算时间长于网格代码；但在三维计算中，GRINN在保持相似精度的情况下，计算时间比网格代码低一个数量级。因此，像GRINN这样的物理信息神经网络在提升三维天体物理流动建模能力方面展现出巨大潜力。