Learned discretizations for passive scalar advection in a two-dimensional turbulent flow
Learned discretizations for passive scalar advection in a two-dimensional turbulent flow
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DOI：
10.1103/physrevfluids.6.064605
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发表时间：
2020-04
影响因子：
2.7
通讯作者：
J. Zhuang;Dmitrii Kochkov;Yohai Bar-Sinai;M. Brenner;Stephan Hoyer
中科院分区：
文献类型：
--
作者：
J. Zhuang;Dmitrii Kochkov;Yohai Bar-Sinai;M. Brenner;Stephan Hoyer
流体模拟的计算成本随着网格分辨率的增加而迅速增加。这给模拟准确解决复杂流动的小尺度特征的能力带来了很大的限制。在这里，我们使用机器学习方法来学习一种数值离散化，即使在经典方法的解决方案分辨率不足的情况下也能保持高精度。我们将这种方法应用于二维湍流中的被动标量平流。该方法保持了与传统高阶通量限制平流求解器相同的精度，同时在每个维度上使用低4倍的网格分辨率。机器学习组件与传统的有限体积方案紧密集成，并且可以通过端到端可微分编程框架进行训练。求解器可以通过卷积滤波器在CPU和加速器上实现接近峰值的硬件利用率。代码可在此https URL上获得
The computational cost of fluid simulations increases rapidly with grid resolution. This has given a hard limit on the ability of simulations to accurately resolve small scale features of complex flows. Here we use a machine learning approach to learn a numerical discretization that retains high accuracy even when the solution is under-resolved with classical methods. We apply this approach to passive scalar advection in a two-dimensional turbulent flow. The method maintains the same accuracy as traditional high-order flux-limited advection solvers, while using $4\times$ lower grid resolution in each dimension. The machine learning component is tightly integrated with traditional finite-volume schemes and can be trained via an end-to-end differentiable programming framework. The solver can achieve near-peak hardware utilization on CPUs and accelerators via convolutional filters. Code is available at this https URL