# Residual Modeling for High-Fidelity Learned Compression of Scientific Data

arXiv: https://arxiv.org/abs/2606.05389 · HTML: https://mlsanity.com/paper/2606.05389/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 26 references that are in the map.
- First posted on arXiv 3 Jun 2026.

## Builds on (most cited first, 9 of 9)

- [Variational image compression with a scale hyperprior](https://mlsanity.com/paper/1802.01436/) (2018)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [LPCNet: Improving Neural Speech Synthesis Through Linear Prediction](https://mlsanity.com/paper/1810.11846/) (2018)
- [SZ3: A Modular Framework for Composing Prediction-Based Error-Bounded Lossy Compressors](https://mlsanity.com/paper/2111.02925/) (2021)
- [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)
- [Attention Based Machine Learning Methods for Data Reduction with Guaranteed Error Bounds](https://mlsanity.com/paper/2409.05357/) (2024)
- [Foundation Model for Lossy Compression of Spatiotemporal Scientific Data](https://mlsanity.com/paper/2412.17184/) (2024)
- [Generative Latent Diffusion for Efficient Spatiotemporal Data Reduction](https://mlsanity.com/paper/2507.02129/) (2025)

## Built on by (most cited first, 2 of 2)

- [Multivariate Scientific Data Compression with Learned Cross-Variable Latent Decorrelation and Autoregressive Entropy Modeling](https://mlsanity.com/paper/2608.30262/) (2026)
- [Neural Residual Modeling for Scientific Data Compression under Guaranteed Error Bounds](https://mlsanity.com/paper/2609.23185/) (2026)

## Abstract (arXiv)

Lossy compression is essential for massive spatiotemporal data from scientific simulations. Learned compressors can achieve high compression ratios at moderate accuracy targets, but their aggregate reconstruction losses do not guarantee accuracy for each block. Existing Guaranteed Autoencoder (GAE) methods add a per-block residual correction by retaining SVD/PCA-style coefficients until the target is met. This works at moderate tolerances, but in the high-fidelity regime with block-level NRMSE from 10^-6 to 10^-4, the number of retained coefficients grows quickly and the correction stream dominates the total rate. We propose a residual-centric view: the learned residual is structurally different from the original scientific field and should be coded with a representation designed for that residual. We introduce two residual coders. LBRC is a deterministic, training-free pipeline that adaptively quantizes the learned residual to the target NRMSE and losslessly encodes the resulting integer residual using 3D Lorenzo differencing, zigzag mapping, bit-plane coding, and entropy coding. NGLR adds a causal neural predictor that outputs a normalized bias for an integer-rounded Lorenzo prediction in the same deterministic integer pipeline, reducing the entropy of the remaining residual code while preserving deterministic decoding. The predictor weights are serialized and counted in the bitstream. Across E3SM, JHTDB, and ERA5 at block-level NRMSE targets from 10^-6 to 10^-4, LBRC improves compression ratio over GAE by 30-60% and is broadly competitive with SZ. NGLR adds a further 10-40% over LBRC and outperforms SZ in the evaluated high-fidelity regime. These results show that residual representations tailored to learned-compressor residuals can preserve the advantage of learned compression when global residual correction becomes rate-dominant.