Lossy Compression of PDE Training Inputs: Field Reconstruction Error Does Not Order the Cost to a Trained Operator

תקציר מקורי באנגליתarXiv:2610.06095v2 Announce Type: replace 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