论文标题
使用可微分流体求解器学习的湍流建模：基于物理的损失功能和优化范围
Learned Turbulence Modelling with Differentiable Fluid Solvers: Physics-based Loss-functions and Optimisation Horizons
论文作者
论文摘要
在本文中，我们根据卷积神经网络训练湍流模型。这些学到的湍流模型改善了在模拟时为不可压缩的Navier-Stokes方程的溶解不足的低分辨率解决方案。我们的研究涉及开发可通过多个求解器步骤的优化梯度传播的可区分数值求解器。这些属性的重要性是通过在训练过程中展开更多求解器步骤的那些模型的出色稳定性和准确性来证明的。此外，我们基于湍流物理学引入损失项，以进一步提高模型的准确性。这种方法应用于三个二维的湍流场景，一种均匀的腐烂湍流情况，一个暂时发展的混合层和空间不断发展的混合层。与无模型模拟相比，我们的模型在长期A-tosterii统计数据方面取得了重大改进，而无需将这些统计数据直接包含在学习目标中。在推论时，我们提出的方法还获得了相似准确的纯粹数值方法的实质性改进。
In this paper, we train turbulence models based on convolutional neural networks. These learned turbulence models improve under-resolved low resolution solutions to the incompressible Navier-Stokes equations at simulation time. Our study involves the development of a differentiable numerical solver that supports the propagation of optimisation gradients through multiple solver steps. The significance of this property is demonstrated by the superior stability and accuracy of those models that unroll more solver steps during training. Furthermore, we introduce loss terms based on turbulence physics that further improve the model accuracy. This approach is applied to three two-dimensional turbulence flow scenarios, a homogeneous decaying turbulence case, a temporally evolving mixing layer, and a spatially evolving mixing layer. Our models achieve significant improvements of long-term a-posteriori statistics when compared to no-model simulations, without requiring these statistics to be directly included in the learning targets. At inference time, our proposed method also gains substantial performance improvements over similarly accurate, purely numerical methods.
