用神经网络模拟原始恒星形成中的热化学演化，速度提升百倍以上。
Neural-Network Chemical Emulator for First-Star Formation: Robust Iterative Predictions over a Wide Density Range
- 分段训练深度算子网络，覆盖21个数量级密度范围。
- 90%以上情况温度与丰度误差低于10%，仅对罕见物种H₂⁺略差。
- 采用基于时间尺度的更新方法，适合长期迭代计算，适合星形成模拟加速。
我们提出一种用于原初恒星形成中热化学演化的神经网络模拟器。该模拟器能准确复现跨越21个数量级（10⁻³–10¹⁸ cm⁻³）的广泛密度范围内的热化学演化过程，追踪六种原初物质：H、H₂、e⁻、H⁺、H⁻、H₂⁺。为应对巨大动态范围，将密度区间分为五个子区域，每个区域分别训练独立的DeepONet。在随机采样的热化学状态上，模拟器对温度和化学丰度的相对误差在90%以上案例中低于10%（除稀有物种H₂⁺外）。相比传统数值积分，该模拟器在CPU上快约十倍，在GPU批量预测时快超过1000倍。为进一步确保多次迭代下的鲁棒性，引入一种基于时间尺度的更新方法：通过缩放长时步预测的变化量，获得短时步更新值，其特征变化时间尺度即为该变量的典型变化周期。在一区坍缩计算中，该方法结果与传统数值积分高度一致，即使在短至自由落体时间10⁻⁴的步长下也表现稳定。本概念验证研究表明，基于神经网络的化学模拟器有望显著加速恒星形成中的流体动力学模拟。
原文摘要 · Abstract (English)
We present a neural-network emulator for the thermal and chemical evolution in Population III star formation. The emulator accurately reproduces the thermochemical evolution over a wide density range spanning 21 orders of magnitude (10$^{-3}$-10$^{18}$ cm$^{-3}$), tracking six primordial species: H, H$_2$, e$^{-}$, H$^{+}$, H$^{-}$, and H$_2^{+}$. To handle the broad dynamic range, we partition the density range into five subregions and train separate deep operator networks (DeepONets) in each region. When applied to randomly sampled thermochemical states, the emulator achieves relative errors below 10% in over 90% of cases for both temperature and chemical abundances (except for the rare species H$_2^{+}$). The emulator is roughly ten times faster on a CPU and more than 1000 times faster for batched predictions on a GPU, compared with conventional numerical integration. Furthermore, to ensure robust predictions under many iterations, we introduce a novel timescale-based update method, where a short-timestep update of each variable is computed by rescaling the predicted change over a longer timestep equal to its characteristic variation timescale. In one-zone collapse calculations, the results from the timescale-based method agree well with traditional numerical integration even with many iterations at a timestep as short as 10$^{-4}$ of the free-fall time. This proof-of-concept study suggests the potential for neural network-based chemical emulators to accelerate hydrodynamic simulations of star formation.
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