  We present a novel technique for hierarchical super resolution (SR) with
neural networks (NNs), which upscales volumetric data represented with an
octree data structure to a high-resolution uniform grid with minimal seam
artifacts on octree node boundaries. Our method uses existing state-of-the-art
SR models and adds flexibility to upscale input data with varying levels of
detail across the domain, instead of only uniform grid data that are supported
in previous approaches. The key is to use a hierarchy of SR NNs, each trained
to perform 2x SR between two levels of detail, with a hierarchical SR algorithm
that minimizes seam artifacts by starting from the coarsest level of detail and
working up. We show that our hierarchical approach outperforms baseline
interpolation and hierarchical upscaling methods, and demonstrate the
usefulness of our proposed approach across three use cases including data
reduction using hierarchical downsampling+SR instead of uniform
downsampling+SR, computation savings for hierarchical finite-time Lyapunov
exponent field calculation, and super-resolving low-resolution simulation
results for a high-resolution approximation visualization.
