共动计算机加速（COCA）：在仿真参考系中的 $N$ 体模拟
COmoving Computer Acceleration (COCA): $N$-body simulations in an emulated frame of reference
AI总结：
COCA 提出一种混合框架，将机器学习与 N 体模拟器结合，在仿真参考系中求解正确运动方程，通过设计纠正仿真误差，减少力评估次数，降低成本并提高预测准确性。
摘要：
$N$ 体模拟计算成本高昂，因此基于机器学习（ML）的仿真技术应运而生，以提高其速度。尽管代理模型速度快，但由于当前方法无法纠正的潜在显著仿真误差，其可信度有限。为解决这一问题，我们引入了共动计算机加速（COCA），这是一个将机器学习与 $N$ 体模拟器接口的混合框架。在仿真参考系中求解正确的物理运动方程，从而通过设计纠正任何仿真误差。该方法对应于求解粒子轨迹围绕机器学习解的扰动，这比获得完整解计算成本更低，但保证随着力评估次数的增加收敛到真实解。尽管该方法适用于任何机器学习算法和 $N$ 体模拟器，但在特定情况下进行了评估，即使用卷积神经网络预测的参考系中的粒子网格宇宙学模拟，其中时间依赖性作为额外的输入参数编码到网络中。COCA 有效减少了粒子轨迹中的仿真误差，所需的力评估次数远少于不使用机器学习运行相应模拟的次数。我们在降低计算预算的情况下获得了准确的最终密度场和速度场。我们证明了该方法在应用于训练数据范围之外的示例时表现出鲁棒性。与使用相同训练资源直接仿真拉格朗日位移场相比，COCA 纠正仿真误差的能力带来了更准确的预测。COCA 通过跳过不必要的力评估使 $N$ 体模拟更便宜，同时仍然求解正确的运动方程并纠正机器学习产生的仿真误差。
英文摘要：
$N$-body simulations are computationally expensive, so machine-learning (ML)-based emulation techniques have emerged as a way to increase their speed. Although fast, surrogate models have limited trustworthiness due to potentially substantial emulation errors that current approaches cannot correct for. To alleviate this problem, we introduce COmoving Computer Acceleration (COCA), a hybrid framework interfacing ML with an $N$-body simulator. The correct physical equations of motion are solved in an emulated frame of reference, so that any emulation error is corrected by design. This approach corresponds to solving for the perturbation of particle trajectories around the machine-learnt solution, which is computationally cheaper than obtaining the full solution, yet is guaranteed to converge to the truth as one increases the number of force evaluations. Although applicable to any ML algorithm and $N$-body simulator, this approach is assessed in the particular case of particle-mesh cosmological simulations in a frame of reference predicted by a convolutional neural network, where the time dependence is encoded as an additional input parameter to the network. COCA efficiently reduces emulation errors in particle trajectories, requiring far fewer force evaluations than running the corresponding simulation without ML. We obtain accurate final density and velocity fields for a reduced computational budget. We demonstrate that this method shows robustness when applied to examples outside the range of the training data. When compared to the direct emulation of the Lagrangian displacement field using the same training resources, COCA's ability to correct emulation errors results in more accurate predictions. COCA makes $N$-body simulations cheaper by skipping unnecessary force evaluations, while still solving the correct equations of motion and correcting for emulation errors made by ML.
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