Statistical Detectability Does Not Imply Predictive Value: Testing Physics-Based Corrections in a Reduced-Order Model of Sediment-Particle Motion

Physics-based correction terms in reduced-order models are often motivated by statistically detectable structure in model residuals, but statistical detectability does not guarantee out-of-sample predictive value. Here, statistical detectability means reproducible evidence that a candidate physical term is associated with residual errors of the baseline particle-motion model; it does not refer to detection of particle entrainment itself. This distinction is examined using a reduced-order, two-state Kalman-filter model of sediment-particle displacement and velocity, applied to synchronous flume measurements of a fully exposed 8 mm Viton sphere undergoing repeated near-threshold rolling entrainment and return within a defined bed pocket. Starting from six candidate terms, validation-likelihood screening identifies statistically supported corrections, whereas a subsequent, test-informed multi-step predictive-parsimony comparison highlights the flow-dependent particle-velocity interaction C = −d2vp|u| as a compact representative correction. At a 1 s horizon, the displacement-increment R2 increases from +0.054 for the physics-only model to +0.168 for this representative corrected model (three-seed means), under conditional forecasts supplied with observed future flow. The interaction is structurally compatible with the cross-term in quadratic relative-velocity drag but is not identified uniquely as drag because it may also absorb unresolved pin-contact and restoring dynamics. The results demonstrate that physical plausibility, statistical detectability, and predictive usefulness are distinct criteria when augmenting reduced-order models of near-threshold sediment-particle motion.