Allocation Entropy for Single-Pass Risk Triage in Neural Operators

The same predicted field can receive a different risk decision when its allocation is read in another basis. Allocation Uncertainty Decomposition (AUD) makes this representation effect measurable in one pass: it reads threshold entropy from wavelet, Fourier, and branch–trunk components, and energy dispersion from selective updates, without changing the predicted field or training a risk head.For threshold adapters, entropy equals conditional uncertainty in component membership under fixed-threshold logistic perturbations; held-out data connect that structural quantity to physical error. On five frozen Haar-trained models, switching the readout to db2 changes $22.5\%$ of accept/reject decisions at $80\%$ coverage. Crossed training finds EM matching gains and a Darcy preference for Haar under either training basis. Four electromagnetic adapters rank in-domain error with five-seed mean correlations of $0.238$–$0.492$; newly trained MWNO and FNO models retain correlations near $0.31$–$0.32$ on advection–diffusion.AUD improves screening over random selection in an independent label-budget test, while inexpensive input controls screen more strongly. At batch 96 on one RTX\ 4090, prediction plus AUD takes $0.513$ ms/sample versus $5.070$ for ten-pass Monte Carlo dropout. These results identify representation choice as a measurable axis of single-pass risk triage.