In recent years, applying deep learning to solve physics problems has attracted much attention. Data-driven deep learning methods produce operators that can learn solutions to the whole system of partial differential equations. However, the existing methods are only evaluated on simple flow equations (e.g., Burger's equation), and only consider the generalization ability on different initial conditions. In this paper, we construct CFDBench, a benchmark with four classic problems in computational fluid dynamics (CFD): lid-driven cavity flow, laminar boundary layer flow in circular tubes, dam flows through the steps, and periodic Karman vortex street. Each flow problem includes data with different boundary conditions, fluid physical properties, and domain geometry. Compared to existing datasets, the advantages of CFDBench are (1) comprehensive. It contains common physical parameters such as velocity, pressure, and cavity fraction. (2) realistic. It is very suitable for deep learning solutions of fluid mechanics equations. (3) challenging. It has a certain learning difficulty, prompting to find models with strong learning ability. (4) standardized. CFDBench facilitates a comprehensive and fair comparison of different deep learning methods for CFD. We make appropriate modifications to popular deep neural networks to apply them to CFDBench and enable the accommodation of more changing inputs. The evaluation on CFDBench reveals some new shortcomings of existing works and we propose possible directions for solving such problems.

近年来，将深度学习应用于解决物理问题引起了广泛关注。本文构建了一个基准测试集CFDBench，其中包含了计算流体动力学中的四个经典问题，并评估了现有方法在不同边界条件、流体物理性质和域几何形状下的泛化能力，用来促进找到具有强大学习能力的模型。

CFDBench：流体力学中机器学习方法的综合基准