Decision-Localized Characteristic Defects for Stochastic Neural Operator Selection

Two stochastic neural operators can agree on global trajectory statistics yet predict different outcomes for the same path-dependent decision. With a small diagnostic-rollout budget, estimating these outcomes directly is noisy. Decision-localized characteristic defects (DLCD) select among pretrained operators by measuring exposure, drift, and covariance-sensitive increment errors in reference-defined decision regions. A fixed bank of physical observables, reusable reference calibration, and trusted local transitions provide the selection signal. At 512 diagnostic paths per candidate-condition, mean held-out regret across eight newly trained stochastic Allen–Cahn pools is 0.02510, compared with 0.02880 for regularized direct event estimation and 0.02693 for localized coefficient matching with matched information sources. The matched-information comparison yields 4.2% lower regret on a second Allen–Cahn cohort and 9.3% on six stochastic 2-D Kolmogorov pools. A history-conditioned decomposition explains the connection between local discrepancies and path decisions; ablations examine localization and aggregation. The gains are concentrated at smaller rollout budgets. Converting measured runtimes into additional direct-estimation paths produces an effective tie.