Neural Stream Functions
Skylar Wolfgang Wurster Hanqi Guo Tom Peterka Han-Wei Shen
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.