论文标题
在二维湍流中学习的被动标量对流的离散
Learned discretizations for passive scalar advection in a 2-D turbulent flow
论文作者
论文摘要
流体模拟的计算成本随着电网分辨率迅速增加。这已经对模拟准确解决复杂流的小规模特征的能力进行了严格的限制。在这里，我们使用一种机器学习方法来学习一种数值离散化，即使解决方案用经典方法不足，该方法仍保持高精度。我们将这种方法应用于二维湍流中的被动标量对流。该方法具有与传统高阶限制对流求解器相同的准确性，同时使用每个维度下的网格分辨率较低。机器学习组件与传统的有限体积方案紧密地集成在一起，可以通过端到端可区分的编程框架进行培训。求解器可以通过卷积过滤器在CPU和加速器上实现近高峰硬件利用率。代码可在https://github.com/google-research/data-driven-pdes上找到。
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 4x 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 https://github.com/google-research/data-driven-pdes.
