From a Single Real-Anchored SEIR Record to an Ensemble of Surveillance Realizations: MAGI Versus Physics-Informed Neural Networks Under Full and Missing–Exposed Observation

This revised manuscript presents a real-calendar-anchored SEIR simulation benchmark for comparing manifold-constrained Gaussian process inference (MAGI) and physics-informed neural networks (PINNs). The study is explicitly positioned as an empirical benchmarking and reproducibility contribution rather than a new epidemic model or a new inference algorithm. A deterministic proportional SEIR system defines the mechanistic truth, while municipal surveillance records motivate the calendar and observation context. We compare full observation of E,I,R with a missing–exposed regime in which only I,R are observed. A parametric bootstrap with independent log-normal measurement noise generates an expanded ensemble (B=80); this ensemble supports bootstrap medians, interquartile ranges, outlier assessment, and sensitivity analysis under the declared measurement-error model. The revision clarifies the role of the PINN data–physics weight λ, the oracle MAGI hyperparameter stabilization used in the missing-E experiment, the distinction between MAP estimates and Bayesian posterior uncertainty, and the operational role of PELT changepoint-guided sparse sampling. The results support a balanced conclusion: MAGI is stable in the fully observed setting, whereas PINNs can be competitive under appropriate λ choices; the missing–exposed case remains ill-posed and requires cautious interpretation.