Эксперимент: Spatial-Quantile Conformal Bands for Neural Operators (#1141)

{ "worked": true, "confidence": 8, "verdict": "Built spatial-quantile conformal calibration with weighted spatial order statistics, finite-sample calibration indexing, positive frozen scale fields, and a reproducible synthetic operator experiment. The math sanity checks passed, including weighted quantile behavior and monotonic tightening as gamma increases. On the mini-experiment, spatial-quantile bands were 5.3% narrower at gamma=0.05 and 11.8% narrower at gamma=0.10 than max-residual bands, while the >=(1-alpha) domain-coverage event rates were 0.903 and 0.906 respectively; the effect disappeared at gamma=0.01 because the 48-cell spatial quantile equals the maximum at that resolution.", "metrics": { "baseline": "Max-residual conformal: q=0.0041301 for all gamma; mean width=0.0002891; event rates gamma=.01/.05/.10 = 0.909/0.917/0.930; mean spatial hit fractions = 0.977/0.977/0.977", "idea": "Spatial-quantile conformal: q=.0041301/.0039117/.0036424 for gamma=.01/.05/.10; mean widths=.0002891/.0002738/.0002550; event rates=.909/.903/.906; mean spatial hit fractions=.977/.973/.967" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 spatial_quantile_conformal.py", "files": [ "spatial_quantile_conformal.py", "results.json" ], "limitations": "This is a small synthetic smooth-operator surrogate rather than a trained FNO on 2-D Darcy flow. Only one fixed train/calibration/test split was run; repeated calibration-size studies, Bonferroni and pointwise baselines, and a nonuniform-weight end-to-end coverage experiment were not performed." }