In recent years, applying deep learning to solve physics problems has attracted much attention. Data-driven deep learning methods produce fast numerical operators that can learn approximate solutions to the whole system of partial differential equations (i.e., surrogate modeling). Although these neural networks may have lower accuracy than traditional numerical methods, they, once trained, are orders of magnitude faster at inference. Hence, one crucial feature is that these operators can generalize to unseen PDE parameters without expensive re-training.In this paper, we construct CFDBench, a benchmark tailored for evaluating the generalization ability of neural operators after training in computational fluid dynamics (CFD) problems. It features four classic CFD problems: lid-driven cavity flow, laminar boundary layer flow in circular tubes, dam flows through the steps, and periodic Karman vortex street. The data contains a total of 302K frames of velocity and pressure fields, involving 739 cases with different operating condition parameters, generated with numerical methods. We evaluate the effectiveness of popular neural operators including feed-forward networks, DeepONet, FNO, U-Net, etc. on CFDBnech by predicting flows with non-periodic boundary conditions, fluid properties, and flow domain shapes that are not seen during training. Appropriate modifications were made to apply popular deep neural networks to CFDBench and enable the accommodation of more changing inputs. Empirical results on CFDBench show many baseline models have errors as high as 300% in some problems, and severe error accumulation when performing autoregressive inference. CFDBench facilitates a more comprehensive comparison between different neural operators for CFD compared to existing benchmarks.

翻译：近年来，将深度学习应用于解决物理问题受到了广泛关注。数据驱动的深度学习方法能够生成快速数值算子，学习偏微分方程整个系统的近似解（即代理建模）。尽管这些神经网络的精度可能低于传统数值方法，但一旦训练完成，其推理速度可提升数个数量级。因此，一个关键特性在于，这些算子能够在不进行昂贵重训练的情况下泛化至未见过的PDE参数。本文构建了CFDBench，这是一个专为评估计算流体动力学问题中神经算子训练后泛化能力而设计的基准测试。它包含四个经典CFD问题：方腔驱动流、圆管层流边界层流、台阶坝水流以及周期性卡门涡街。数据共计包含302K帧速度场与压力场，涉及739种不同工况参数组合，均采用数值方法生成。我们评估了包括前馈网络、DeepONet、FNO、U-Net等在内的流行神经算子在CFDBench上的有效性，通过预测训练中未出现的非周期性边界条件、流体性质及流场区域形状来测试其性能。为适应CFDBench并支持更多可变输入，我们对流行的深度神经网络进行了适当修改。CFDBench上的实验结果表明，多个基线模型在某些问题中的误差高达300%，且在自回归推理时存在严重的误差累积问题。与现有基准测试相比，CFDBench能够更全面地比较不同神经算子在CFD问题中的表现。