  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.
