# Neural Residual Modeling for Scientific Data Compression under Guaranteed Error Bounds

arXiv: https://arxiv.org/abs/2609.23185 · HTML: https://mlsanity.com/paper/2609.23185/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 35 references that are in the map.
- First posted on arXiv 19 Sep 2026.

## Builds on (most cited first, 23 of 23)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Variational image compression with a scale hyperprior](https://mlsanity.com/paper/1802.01436/) (2018)
- [SoundStream: An End-to-End Neural Audio Codec](https://mlsanity.com/paper/2107.03312/) (2021)
- [High Fidelity Neural Audio Compression](https://mlsanity.com/paper/2210.13438/) (2022)
- [Full Resolution Image Compression with Recurrent Neural Networks](https://mlsanity.com/paper/1608.05148/) (2016)
- [Improved Lossy Image Compression with Priming and Spatially Adaptive Bit Rates for Recurrent Networks](https://mlsanity.com/paper/1703.10114/) (2017)
- [A Unified End-to-End Framework for Efficient Deep Image Compression](https://mlsanity.com/paper/2002.03370/) (2020)
- [SZ3: A Modular Framework for Composing Prediction-Based Error-Bounded Lossy Compressors](https://mlsanity.com/paper/2111.02925/) (2021)
- [Deep Lossy Plus Residual Coding for Lossless and Near-lossless Image Compression](https://mlsanity.com/paper/2209.04847/) (2022)
- [Exploring Autoencoder-based Error-bounded Compression for Scientific Data](https://mlsanity.com/paper/2105.11730/) (2021)
- [MGARD: A multigrid framework for high-performance, error-controlled data compression and refactoring](https://mlsanity.com/paper/2401.05994/) (2024)
- [SRN-SZ: Deep Leaning-Based Scientific Error-bounded Lossy Compression with Super-resolution Neural Networks](https://mlsanity.com/paper/2309.04037/) (2023)
- [Attention Based Machine Learning Methods for Data Reduction with Guaranteed Error Bounds](https://mlsanity.com/paper/2409.05357/) (2024)
- [GWLZ: A Group-wise Learning-based Lossy Compression Framework for Scientific Data](https://mlsanity.com/paper/2404.13470/) (2024)
- [Machine Learning Techniques for Data Reduction of Climate Applications](https://mlsanity.com/paper/2405.00879/) (2024)
- [NeurLZ: An Online Neural Learning-Based Method to Enhance Scientific Lossy Compression](https://mlsanity.com/paper/2409.05785/) (2024)
- [Guaranteed Conditional Diffusion: 3D Block-based Models for Scientific Data Compression](https://mlsanity.com/paper/2502.12951/) (2025)
- [Residual Modeling for High-Fidelity Learned Compression of Scientific Data](https://mlsanity.com/paper/2606.05389/) (2026)
- [Learned Compression Artifact Removal by Deep Residual Networks](https://mlsanity.com/paper/1806.00333/) (2018)

## Abstract (arXiv)

Lossy compression of scientific simulation data increasingly relies on learned, latent-space architectures such as Residual Vector Quantization (RVQ), which iteratively quantize a base representation and its residuals to progressively reduce reconstruction error. While effective, RVQ performs this residual modeling entirely in latent space, leaving the pixel-space error structure of the reconstruction largely unaddressed. In this work, we propose a post-processing pipeline that augments an RVQ-based compressor with a U-Net trained to predict and correct pixel-space residuals between the original volume and its RVQ reconstruction. We show that these residuals are spatially structured rather than driven by local intensity or gradient features, motivating the need for a deep spatial model rather than simple statistical correction. The U-Net-corrected reconstruction is then passed through a Guaranteed Autoencoder (GAE) stage, which projects the remaining residual onto a per-block PCA basis to enforce a user-specified block-wise error bound. To the best of our knowledge, this is the first pipeline to combine latent-space RVQ, explicit pixel-space residual correction via a deep spatial post-processing network, and GAE-based error-bound guarantees within a single framework for scientific data compression. We evaluate our approach on S3D, JHTDB and E3SM datasets, demonstrating consistent improvements in NRMSE, compression ratio] over RVQ-only and standard residual-correction baselines, while maintaining strict error guarantees required for scientific data fidelity.