# Deep Hierarchical Super Resolution for Scientific Data

arXiv: https://arxiv.org/abs/2107.00462 · HTML: https://mlsanity.com/paper/2107.00462/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 67 references that are in the map.
- First posted on arXiv 30 May 2021.

## Builds on (most cited first, 22 of 22)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network](https://mlsanity.com/paper/1609.05158/) (2016)
- [Accurate Image Super-Resolution Using Very Deep Convolutional Networks](https://mlsanity.com/paper/1511.04587/) (2015)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [Accelerating the Super-Resolution Convolutional Neural Network](https://mlsanity.com/paper/1608.00367/) (2016)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Deep Learning for Image Super-resolution: A Survey](https://mlsanity.com/paper/1902.06068/) (2019)
- [OctNet: Learning Deep 3D Representations at High Resolutions](https://mlsanity.com/paper/1611.05009/) (2016)
- [Octree Generating Networks: Efficient Convolutional Architectures for High-resolution 3D Outputs](https://mlsanity.com/paper/1703.09438/) (2017)
- [Fast and Accurate Image Super-Resolution with Deep Laplacian Pyramid Networks](https://mlsanity.com/paper/1710.01992/) (2017)
- [TTHRESH: Tensor Compression for Multidimensional Visual Data](https://mlsanity.com/paper/1806.05952/) (2018)
- [InSituNet: Deep Image Synthesis for Parameter Space Exploration of Ensemble Simulations](https://mlsanity.com/paper/1908.00407/) (2019)
- [Deformable Non-local Network for Video Super-Resolution](https://mlsanity.com/paper/1909.10692/) (2019)
- [Exploring Autoencoder-based Error-bounded Compression for Scientific Data](https://mlsanity.com/paper/2105.11730/) (2021)
- [Volumetric Isosurface Rendering with Deep Learning-Based Super-Resolution](https://mlsanity.com/paper/1906.06520/) (2019)
- [Learning Adaptive Sampling and Reconstruction for Volume Visualization](https://mlsanity.com/paper/2007.10093/) (2020)
- [MGARD+: Optimizing Multilevel Methods for Error-bounded Scientific Data Reduction](https://mlsanity.com/paper/2010.05872/) (2020)
- [AMM: Adaptive Multilinear Meshes](https://mlsanity.com/paper/2007.15219/) (2020)

## Built on by (most cited first, 12 of 12)

- [Super-Resolution Analysis via Machine Learning: A Survey for Fluid Flows](https://mlsanity.com/paper/2301.10937/) (2023)
- [Interactive Volume Visualization via Multi-Resolution Hash Encoding based Neural Representation](https://mlsanity.com/paper/2207.11620/) (2022)
- [ECNR: Efficient Compressive Neural Representation of Time-Varying Volumetric Datasets](https://mlsanity.com/paper/2311.12831/) (2023)
- [PSRFlow: Probabilistic Super Resolution with Flow-Based Models for Scientific Data](https://mlsanity.com/paper/2308.04605/) (2023)
- [Uncertainty-Aware Deep Neural Representations for Visual Analysis of Vector Field Data](https://mlsanity.com/paper/2407.16119/) (2024)
- [Uncertainty-Informed Volume Visualization using Implicit Neural Representation](https://mlsanity.com/paper/2408.06018/) (2024)
- [CD-TVD: Contrastive Diffusion for 3D Super-Resolution with Scarce High-Resolution Time-Varying Data](https://mlsanity.com/paper/2508.08173/) (2025)
- [Visual Analysis of Prediction Uncertainty in Neural Networks for Deep Image Synthesis](https://mlsanity.com/paper/2406.18545/) (2024)
- [Topology Guidance: Controlling the Outputs of Generative Models via Vector Field Topology](https://mlsanity.com/paper/2505.06804/) (2025)
- [REV-INR: Regularized Evidential Implicit Neural Representation for Uncertainty-Aware Volume Visualization](https://mlsanity.com/paper/2601.17689/) (2026)
- [Compressive Modeling and Visualization of Multivariate Scientific Data using Implicit Neural Representation](https://mlsanity.com/paper/2510.15535/) (2025)
- [From Scalars to Time Series: Rethinking Implicit Neural Representations for Time-Varying Volumetric Data](https://mlsanity.com/paper/2607.20970/) (2026)

## Abstract (arXiv)

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.