# Compressive Neural Representations of Volumetric Scalar Fields

arXiv: https://arxiv.org/abs/2104.04523 · HTML: https://mlsanity.com/paper/2104.04523/

## Key facts

- Cited by 64 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 56 references that are in the map.
- First posted on arXiv 11 Apr 2021.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Texture Fields: Learning Texture Representations in Function Space](https://mlsanity.com/paper/1905.07259/) (2019)
- [SDFDiff: Differentiable Rendering of Signed Distance Fields for 3D Shape Optimization](https://mlsanity.com/paper/1912.07109/) (2019)
- [DualSDF: Semantic Shape Manipulation using a Two-Level Representation](https://mlsanity.com/paper/2004.02869/) (2020)
- [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)
- [A Generative Model for Volume Rendering](https://mlsanity.com/paper/1710.09545/) (2017)
- [On the Effectiveness of Weight-Encoded Neural Implicit 3D Shapes](https://mlsanity.com/paper/2009.09808/) (2020)
- [Volumetric Isosurface Rendering with Deep Learning-Based Super-Resolution](https://mlsanity.com/paper/1906.06520/) (2019)
- [Topologically Controlled Lossy Compression](https://mlsanity.com/paper/1802.02731/) (2018)

## Built on by (most cited first, 30 of 64)

- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Variable Bitrate Neural Fields](https://mlsanity.com/paper/2206.07707/) (2022)
- [COIN++: Neural Compression Across Modalities](https://mlsanity.com/paper/2201.12904/) (2022)
- [C3: High-performance and low-complexity neural compression from a single image or video](https://mlsanity.com/paper/2312.02753/) (2023)
- [Generalizable Implicit Neural Representations via Instance Pattern Composers](https://mlsanity.com/paper/2211.13223/) (2022)
- [Neural Implicit Flow: a mesh-agnostic dimensionality reduction paradigm of spatio-temporal data](https://mlsanity.com/paper/2204.03216/) (2022)
- [Fast Neural Representations for Direct Volume Rendering](https://mlsanity.com/paper/2112.01579/) (2021)
- [DL4SciVis: A State-of-the-Art Survey on Deep Learning for Scientific Visualization](https://mlsanity.com/paper/2204.06504/) (2022)
- [Compressing multidimensional weather and climate data into neural networks](https://mlsanity.com/paper/2210.12538/) (2022)
- [On Quantizing Implicit Neural Representations](https://mlsanity.com/paper/2209.01019/) (2022)
- [Interactive Volume Visualization via Multi-Resolution Hash Encoding based Neural Representation](https://mlsanity.com/paper/2207.11620/) (2022)
- [HyperINR: A Fast and Predictive Hypernetwork for Implicit Neural Representations via Knowledge Distillation](https://mlsanity.com/paper/2304.04188/) (2023)
- [Compact Neural Graphics Primitives with Learned Hash Probing](https://mlsanity.com/paper/2312.17241/) (2023)
- [iVR-GS: Inverse Volume Rendering for Explorable Visualization via Editable 3D Gaussian Splatting](https://mlsanity.com/paper/2504.17954/) (2025)
- [ECNR: Efficient Compressive Neural Representation of Time-Varying Volumetric Datasets](https://mlsanity.com/paper/2311.12831/) (2023)
- [Adaptively Placed Multi-Grid Scene Representation Networks for Large-Scale Data Visualization](https://mlsanity.com/paper/2308.02494/) (2023)
- [TINC: Tree-structured Implicit Neural Compression](https://mlsanity.com/paper/2211.06689/) (2022)
- [FreSh: Frequency Shifting for Accelerated Neural Representation Learning](https://mlsanity.com/paper/2410.05050/) (2024)
- [SCI: A Spectrum Concentrated Implicit Neural Compression for Biomedical Data](https://mlsanity.com/paper/2209.15180/) (2022)
- [Meta-INR: Efficient Encoding of Volumetric Data via Meta-Learning Implicit Neural Representation](https://mlsanity.com/paper/2502.09669/) (2025)
- [ParaView-MCP: An Autonomous Visualization Agent with Direct Tool Use](https://mlsanity.com/paper/2505.07064/) (2025)
- [StyleRF-VolVis: Style Transfer of Neural Radiance Fields for Expressive Volume Visualization](https://mlsanity.com/paper/2408.00150/) (2024)
- [Distributed Neural Representation for Reactive in situ Visualization](https://mlsanity.com/paper/2304.10516/) (2023)
- [Explorable INR: An Implicit Neural Representation for Ensemble Simulation Enabling Efficient Spatial and Parameter Exploration](https://mlsanity.com/paper/2504.00904/) (2025)
- [SRN-SZ: Deep Leaning-Based Scientific Error-bounded Lossy Compression with Super-resolution Neural Networks](https://mlsanity.com/paper/2309.04037/) (2023)
- [CodecNeRF: Toward Fast Encoding and Decoding, Compact, and High-quality Novel-view Synthesis](https://mlsanity.com/paper/2404.04913/) (2024)
- [Regularized Multi-Decoder Ensemble for an Error-Aware Scene Representation Network](https://mlsanity.com/paper/2407.19082/) (2024)
- [HyperFLINT: Hypernetwork-based Flow Estimation and Temporal Interpolation for Scientific Ensemble Visualization](https://mlsanity.com/paper/2412.04095/) (2024)
- [FFEINR: Flow Feature-Enhanced Implicit Neural Representation for Spatio-temporal Super-Resolution](https://mlsanity.com/paper/2308.12508/) (2023)
- [MC-INR: Efficient Encoding of Multivariate Scientific Simulation Data using Meta-Learning and Clustered Implicit Neural Representations](https://mlsanity.com/paper/2507.02494/) (2025)

## Abstract (arXiv)

We present an approach for compressing volumetric scalar fields using implicit neural representations. Our approach represents a scalar field as a learned function, wherein a neural network maps a point in the domain to an output scalar value. By setting the number of weights of the neural network to be smaller than the input size, we achieve compressed representations of scalar fields, thus framing compression as a type of function approximation. Combined with carefully quantizing network weights, we show that this approach yields highly compact representations that outperform state-of-the-art volume compression approaches. The conceptual simplicity of our approach enables a number of benefits, such as support for time-varying scalar fields, optimizing to preserve spatial gradients, and random-access field evaluation. We study the impact of network design choices on compression performance, highlighting how simple network architectures are effective for a broad range of volumes.