用神经网络直接解吸积盘动力学方程，免数据训练，快且无边界反射误差。
Neural Networks as Surrogate Solvers for Time-Dependent Accretion Disk Dynamics
- 用物理信息神经网络直接求解二维吸积盘流体方程，不依赖观测数据。
- 成功模拟出螺旋密度波激发传播和伴星导致的间隙形成等关键现象。
- 无需人工设置边界，自然避免数值模拟中的边缘反射伪影，适合天体物理建模。
吸积盘广泛存在于行星形成系统、X射线双星及活动星系核等天体物理环境中。传统建模依赖计算量巨大的（磁）流体动力学模拟。近期，物理信息神经网络（PINNs）成为有前景的替代方法，可直接基于物理定律训练神经网络而无需数据。本文首次将PINNs应用于非自引力吸积盘的二维时变流体动力学求解。模型可在训练域内任意时间与位置给出解，并成功复现螺旋密度波的激发与传播、以及伴星相互作用引起的间隙形成等关键物理现象。尤为关键的是，由PINNs实现的无边界方法天然消除了传统数值模拟中难以抑制的盘边缘虚假波反射问题。结果表明，先进机器学习技术可实现无数据驱动的物理建模，未来或可替代传统数值模拟方法。
原文摘要 · Abstract (English)
Accretion disks are ubiquitous in astrophysics, appearing in diverse environments from planet-forming systems to X-ray binaries and active galactic nuclei. Traditionally, modeling their dynamics requires computationally intensive (magneto)hydrodynamic simulations. Recently, Physics-Informed Neural Networks (PINNs) have emerged as a promising alternative. This approach trains neural networks directly on physical laws without requiring data. We for the first time demonstrate PINNs for solving the two-dimensional, time-dependent hydrodynamics of non-self-gravitating accretion disks. Our models provide solutions at arbitrary times and locations within the training domain, and successfully reproduce key physical phenomena, including the excitation and propagation of spiral density waves and gap formation from disk-companion interactions. Notably, the boundary-free approach enabled by PINNs naturally eliminates the spurious wave reflections at disk edges, which are challenging to suppress in numerical simulations. These results highlight how advanced machine learning techniques can enable physics-driven, data-free modeling of complex astrophysical systems, potentially offering an alternative to traditional numerical simulations in the future.
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