arXiv：cs.LG· Huy Hoang Le·· 6 小时前AI 评分38
有损压缩 PDE 训练输入：场重建误差无法决定已训练算子的代价
Lossy Compression of PDE Training Inputs: Field Reconstruction Error Does Not Order the Cost to a Trained Operator
AI 导读
针对算子学习基准以全精度存储、规模已达 TB 级的问题，研究显示输入场的重建误差并不决定压缩数据训练出的算子精度。在均方误差目标下，重建误差在 104 次代价比较中颠倒了 36 次排序，而基于相同前向传播构建的探针只颠倒 12 次；PDEBench 中初始条件相同的两个 PDE 家族在同一场误差下下游差异达三倍。
正文
Abstract:Operator-learning benchmarks are stored at full precision and have grown to terabyte scale. Rate-distortion theory says how many bits the stored field needs, while a practitioner needs to know how accurate an operator trained on the compressed data will be. We show that the first does not determine the second, and measure why, compressing the input fields while targets and test inputs stay at full precision. A solution operator attenuates a perturbation of its input. Pushing a compressed field through a surrogate already trained at full precision measures how much of the perturbation that surrogate transmits. The fraction is consistent with the smoothing behaviour of the underlying equation, and it spans more than two orders of magnitude across PDE families. Field reconstruction error is computed before the attenuation and cannot see it. For operators trained with mean squared error it inverts 36 of 104 cost comparisons across datasets, where a probe built from the same forward passes inverts 12. Two families that PDEBench stores with identical initial conditions differ threefold downstream at identical field error. Under the relative-L2 objective of the reference recipe the separation narrows, while the ordering of the family-level median transmission factors is unchanged. After one full-precision training run, the probe evaluates an entire rate curve by forward passes alone. It ranks datasets and rates consistently across the codecs and architectures we test, while its magnitude does not transfer between them.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.06095 [cs.LG] |
| (or arXiv:2610.06095v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.06095 arXiv-issued DOI via DataCite |
Submission history
From: Huy Hoang Le [view email]
[v1]
Mon, 5 Oct 2026 10:28:46 UTC (240 KB)
[v2]
Tue, 6 Oct 2026 14:03:35 UTC (233 KB)
来源：arXiv：cs.LG · arxiv.org