CSBOO: A Coherent Schrodinger-Bridge-Inspired Orbit Operator for Reliability-Aware Multi-Period Spatio-Temporal Forecasting

Spatio-temporal forecasting often combines recent, daily, and weekly histories, but their reliability changes during incidents and holidays and across forecast horizons; unconstrained mixtures also make orbit weights ambiguous. We present the Coherent Schrödinger-Bridge-Inspired Orbit Operator (CSBOO), which replaces independent reference fusion with sequential inference over the responsibilities of three semantically anchored predictive orbits. A temporally causal backbone constructs horizon states through input-dependent directed spatial propagation, retarded attention, and known calendar phase. The retarded weights also define level, slope, and cross-period mismatch as reliability evidence. A Markov transition propagates responsibility, and a mismatch-informed Feynman–Kac potential corrects it for each sample, node, and horizon. Bounded candidate deformations and target-conditioned calibration give the normalized marginals predictive semantics; their convex barycenter yields the forecast. Across ten tasks, CSBOO achieves the best result in 18 of 20 MAE/RMSE comparisons, including 7.9% lower MAE and 4.0% lower RMSE on PeMS08 than the strongest baseline, with consistent degradation across all reported ablations.