Modeling how supermassive black holes co-evolve with their host galaxies is notoriously hard because the relevant physics spans nine orders of magnitude in scale-from milliparsecs to megaparsecs--making end-to-end first-principles simulation infeasible. To characterize the feedback from the small scales, existing methods employ a static subgrid scheme or one based on theoretical guesses, which usually struggle to capture the time variability and derive physically faithful results. Neural operators are a class of machine learning models that achieve significant speed-up in simulating complex dynamics. We introduce a neural-operator-based ''subgrid black hole'' that learns the small-scale local dynamics and embeds it within the direct multi-level simulations. Trained on small-domain (general relativistic) magnetohydrodynamic data, the model predicts the unresolved dynamics needed to supply boundary conditions and fluxes at coarser levels across timesteps, enabling stable long-horizon rollouts without hand-crafted closures. Thanks to the great speedup in fine-scale evolution, our approach for the first time captures intrinsic variability in accretion-driven feedback, allowing dynamic coupling between the central black hole and galaxy-scale gas. This work reframes subgrid modeling in computational astrophysics with scale separation and provides a scalable path toward data-driven closures for a broad class of systems with central accretors.

翻译：模拟超大质量黑洞如何与其宿主星系协同演化是公认的难题，因为相关物理过程跨越了从毫秒差距到百万秒差距的九个数量级尺度，使得基于第一性原理的端到端模拟不可行。为刻画小尺度反馈，现有方法采用静态的亚网格方案或基于理论猜测的方案，通常难以捕捉时间变异性并获得物理上可信的结果。神经算子是一类机器学习模型，可在模拟复杂动力学过程中实现显著的加速。我们提出一种基于神经算子的“亚网格黑洞”，它学习小尺度局部动力学并将其嵌入到直接多层级模拟中。该模型基于小尺度域（广义相对论性）磁流体动力学数据进行训练，可预测跨时间步长在较粗尺度上所需的未解析动力学，以提供边界条件和通量，从而实现无需人工构造闭合项的稳定长时程推演。得益于精细尺度演化的大幅加速，我们的方法首次捕捉到吸积驱动反馈的内在变异性，实现了中心黑洞与星系尺度气体间的动态耦合。这项工作以尺度分离的方式重构了计算天体物理学中的亚网格建模，为具有中心吸积体的一类广泛系统提供了可扩展的数据驱动闭合方案路径。