We present a neural network approach to compute stream functions, which are
scalar functions with gradients orthogonal to a given vector field. As a
result, isosurfaces of the stream function extract stream surfaces, which can
be visualized to analyze flow features. Our approach takes a vector field as
input and trains an implicit neural representation to learn a stream function
for that vector field. The network learns to map input coordinates to a stream
function value by minimizing the inner product of the gradient of the neural
network's output and the vector field. Since stream function solutions may not
be unique, we give optional constraints for the network to learn particular
stream functions of interest. Specifically, we introduce regularizing loss
functions that can optionally be used to generate stream function solutions
whose stream surfaces follow the flow field's curvature, or that can learn a
stream function that includes a stream surface passing through a seeding rake.
We also discuss considerations for properly visualizing the trained implicit
network and extracting artifact-free surfaces. We compare our results with
other implicit solutions and present qualitative and quantitative results for
several synthetic and simulated vector fields.

本文提出了一种使用神经网络计算流函数的方法，并介绍了使用该方法可视化流场及分析流动特征的流面，其中网络的损失函数可以选择以流线曲率为约束条件来获得特定的流函数解，详细探讨了训练后提取流面的方法，并提出了与其他隐式解决方案的对比和结果。