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This paper introduces TOPIQ, a statistical error-propagation framework designed to predict bias and uncertainty in quantities of interest (QoIs) derived from lossy compressed scientific data. By utilizing compact compression metadata and decomposing QoIs into primitive operators with closed-form propagation rules, TOPIQ effectively manages spatial error correlation and data-error coupling. The framework achieves well-calibrated predictions in 93.1% of configurations across extensive evaluations, significantly enhancing computational efficiency with speedups of 56x-402x for uncertainty quantification.
TOPIQ transforms how we handle uncertainty in scientific data by enabling rapid, well-calibrated predictions from lossy compression metadata.
Lossy compression is essential for managing massive scientific data, but per-element error bounds do not translate into bounds on downstream quantities of interest (QoIs) such as regional averages, neural network predictions, or multi-field derived quantities. We present TOPIQ, a statistical error-propagation framework that predicts QoI-level bias and uncertainty from compact compression metadata (less than 0.1% of original data). TOPIQ decomposes QoIs into primitive operators with closed-form propagation rules accounting for spatial error correlation and data-error coupling; new QoIs are supported by composition at runtime with no per-QoI derivation or retraining. Across 552 evaluations spanning 4 datasets, 3 compressors, 4 QoI families, and 8 error bounds, 93.1% of configurations achieve well-calibrated predictions. Pre-computed metadata enables post-hoc uncertainty quantification for arbitrary query regions at 56x-402x speedup over direct computation. A case study demonstrates integration into an AI-driven analysis pipeline with end-to-end confidence intervals for dynamically composed queries.
