Polynomial-chaos surrogates get locally adaptive intervals: high-noise regions stop being under-covered, from a single fit
Polynomial chaos expansions have long offered only global error metrics, leaving the reliability of an individual prediction unstated; normalizing jackknife+ conformal nonconformity scores with an auxiliary polynomial chaos model makes interval width follow local input uncertainty. For fixed-basis, least-squares-fitted expansions every quantity is available in closed form, so the finite-sample jackknife+ coverage guarantee is retained without retraining; on a cantilever-beam benchmark with known heteroscedastic noise and on steam-generator clogging simulation data, the adaptive intervals reach target coverage and clearly outperform non-adaptive ones in high-uncertainty regions.