Online Bayesian Calibration under Gradual and Abrupt System Changes

Bayesian model calibration is central to digital twins and computer experiments, as it aligns model outputs with field observations by estimating calibration parameters and correcting systematic model bias. Classical Bayesian calibration introduces latent parameters and a discrepancy function to capture bias, but suffers from parameter–discrepancy confounding and is typically formulated as an offline procedure under a stationary data-generating assumption. These limitations are restrictive in modern digital twin applications, where systems evolve over time and may exhibit both gradual drift and abrupt regime shifts. While data assimilation methods enable sequential updates, they generally do not explicitly model systematic bias and are not robust to abrupt changes. We propose Bayesian Recursive Projected Calibration (BRPC), an online Bayesian calibration framework for streaming data under simulator mismatch and nonstationarity. BRPC extends projected calibration to the online setting by separating a discrepancy-free particle update for calibration parameters from a conditional Gaussian process update for discrepancy, preserving identifiability while enabling bias-aware adaptation under gradual system evolution. To handle abrupt changes, we integrate BRPC with restart mechanisms that detect regime shifts and reset the calibration process, yielding a unified approach to mixed nonstationarity. We establish theoretical guarantees for both components, including tracking performance under gradual evolution and false-alarm and detection behavior for restart mechanisms. Empirical results on synthetic and plant-simulation benchmarks demonstrate that BRPC improves calibration accuracy under gradual changes, while the restart-augmented framework further enhances robustness and predictive performance under abrupt regime shifts compared to sliding-window Bayesian calibration and data assimilation baselines.