标题： 共动计算机加速（COCA）：在模拟参考系中的$N$体模拟 显示英文标题

标题： COmoving Computer Acceleration (COCA): $N$-body simulations in an emulated frame of reference

摘要： $N$体模拟计算成本高昂，因此基于机器学习（ML）的仿真技术作为一种提高其速度的方式应运而生。尽管速度快，但代理模型由于当前方法无法修正的潜在重大仿真误差，其可信度有限。为了解决这个问题，我们引入了共动计算机加速（COCA），这是一种结合了机器学习与$N$体模拟器的混合框架。在仿真的参考系中正确求解物理运动方程，从而使任何仿真误差通过设计得到纠正。这种方法相当于求解粒子轨迹相对于机器学习得出的解的扰动，这比获取完整解更节省计算资源，同时随着力评估次数的增加，可以保证收敛到真实值。虽然该方法适用于任何机器学习算法和$N$体模拟器，但在卷积神经网络预测的参考系中对粒子网格宇宙学模拟进行评估时效果最佳，在此情况下，时间依赖性被编码为网络的一个额外输入参数。COCA有效减少了粒子轨迹中的仿真误差，所需力评估次数远少于未使用机器学习运行相应模拟所需的次数。我们以更低的计算预算获得了准确的最终密度和速度场。我们证明，当应用于训练数据范围之外的例子时，该方法仍然表现出稳健性。与直接利用相同训练资源对拉格朗日位移场进行仿真相比，COCA纠正仿真误差的能力导致了更准确的预测。COCA通过跳过不必要的力评估，使$N$体模拟更加经济，同时仍能正确求解运动方程并修正机器学习造成的仿真误差。 显示英文摘要

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.