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.

翻译：我们提出了一种用于计算流函数的神经网络方法，流函数是一种梯度与给定向量场正交的标量函数。由此，流函数的等值面可提取出流面，通过可视化流面可分析流场特征。该方法以向量场为输入，训练隐式神经表示来学习该向量场的流函数。网络通过最小化神经网络输出梯度与向量场的内积，学习将输入坐标映射为流函数值。由于流函数解可能不唯一，我们提供了可选约束条件，使网络能够学习感兴趣的特定流函数。具体而言，我们引入了正则化损失函数，可选择用于生成流面沿流场曲率分布的流函数解，或学习包含经过种子耙的流面的流函数。我们还讨论了正确可视化训练后隐式网络并提取无伪影表面的注意事项。我们将本方法与其他隐式解进行了对比，并给出了多个合成及模拟向量场的定性与定量结果。