# Transmission Factors for Lossy Compression of PDE Training Data: Measuring What Reaches a Trained Operator

arXiv: https://arxiv.org/abs/2610.06095 · HTML: https://mlsanity.com/paper/2610.06095/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 25 references that are in the map.
- First posted on arXiv 5 Oct 2026.

## Builds on (most cited first, 15 of 15)

- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Beyond neural scaling laws: beating power law scaling via data pruning](https://mlsanity.com/paper/2206.14486/) (2022)
- [PDEBENCH: An Extensive Benchmark for Scientific Machine Learning](https://mlsanity.com/paper/2210.07182/) (2022)
- [Deep Learning with Limited Numerical Precision](https://mlsanity.com/paper/1502.02551/) (2015)
- [The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learning](https://mlsanity.com/paper/2412.00568/) (2024)
- [SZ3: A Modular Framework for Composing Prediction-Based Error-Bounded Lossy Compressors](https://mlsanity.com/paper/2111.02925/) (2021)
- [Data Complexity Estimates for Operator Learning](https://mlsanity.com/paper/2405.15992/) (2024)
- [Operator Learning of Lipschitz Operators: An Information-Theoretic Perspective](https://mlsanity.com/paper/2406.18794/) (2024)
- [The Sample Complexity of Learning Lipschitz Operators with respect to Gaussian Measures](https://mlsanity.com/paper/2410.23440/) (2024)
- [SRN-SZ: Deep Leaning-Based Scientific Error-bounded Lossy Compression with Super-resolution Neural Networks](https://mlsanity.com/paper/2309.04037/) (2023)
- [Understanding The Effectiveness of Lossy Compression in Machine Learning Training Sets](https://mlsanity.com/paper/2403.15953/) (2024)
- [Towards Sharp Minimax Risk Bounds for Operator Learning](https://mlsanity.com/paper/2512.17805/) (2025)
- [Quantifying the Impact of Lossy Compression on Neural Generative Surrogate Modeling](https://mlsanity.com/paper/2606.15959/) (2026)

## Abstract (arXiv)

Operator-learning benchmarks ship as full-precision arrays, and they have grown to terabyte scale. A curator who wants to distribute one has to decide how coarsely to store it. That decision is usually made by fixing a tolerance on the reconstruction error of the stored field. We show that this quantity is measured in the wrong place. It compares the stored field with the original, before any model is trained. What the curator is buying is the accuracy of a model trained on the compressed copy, and the two can disagree: two PDEBench families stored to identical field error differ threefold downstream. A solution operator smooths, so only part of the codec error ever reaches the model's output. That part can be measured. Push a compressed field through a model already trained at full precision, and compare its output against the output on the clean field. The measurement costs forward passes and no training on compressed data. It spans more than two orders of magnitude across six PDE families, and it orders downstream cost where field error does not, inverting 12 of 104 cross-dataset comparisons against field error's 36. Read as a budget, the same curve nominates a storage rate for each dataset. A back-check against trained models finds those rates wrong in both directions by up to a factor of two in stored bits.