Uncertainty and decision reliability in physics-informed engineering predictions

Abstract

Physics-informed predictions require uncertainty statements tied to the engineering quantity and decision being supported. Small average field error does not establish calibrated uncertainty in a peak temperature, integrated force, inferred parameter, or defect classification. This review distinguishes observation error, uncertainty within a model family, physical discrepancy, and numerical approximation. It compares Bayesian, ensemble, and conformal approaches according to their assumptions and develops analytical examples for correlated field integration, simultaneous coverage, exact physical constraints, and rare-event validation. A proposed assessment protocol separates calibration from testing and evaluates uncertainty under operating shifts, sensor faults, and downstream threshold decisions.