Online Bayesian Calibration under Gradual and Abrupt System Changes

2026-05-07

AI Summary

Traditional Bayesian calibration struggles in dynamic systems to disentangle model parameters from discrepancy terms and is ill-equipped to handle both gradual drifts and abrupt shifts, often being confined to offline settings. This work proposes the Bayesian Recursive Projection Calibration (BRPC) framework, which extends projection-based calibration to online scenarios for the first time. BRPC ensures identifiability and tracks gradual changes by decoupling parameter updates from discrepancy modeling via Gaussian processes, while incorporating a theoretically grounded restart mechanism coupled with online change detection to respond to sudden shifts. Experimental results on synthetic data and industrial process simulations demonstrate that BRPC significantly outperforms sliding-window Bayesian calibration and data assimilation baselines, achieving higher accuracy under gradual drift and maintaining robustness during abrupt changes.

Abstract

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 model 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 gradual drift and abrupt regime shifts. While data assimilation methods enable sequential updates, they generally do not explicitly model systematic bias and are less effective under 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, BRPC is integrated with restart mechanisms that detect regime shifts and reset the calibration process. We establish theoretical guarantees for both components, including tracking performance under gradual evolution and false-alarm and detection behavior for restart mechanisms. Empirical studies on synthetic and plant-simulation benchmarks show that BRPC improves calibration accuracy under gradual changes, while restart-augmented BRPC further improves robustness and predictive performance under abrupt regime shifts compared to sliding-window Bayesian calibration and data assimilation baselines.

Problem

• Bayesian calibration
• nonstationarity
• systematic bias
• regime shifts
• digital twins

Innovation

• Bayesian calibration
• online learning
• discrepancy modeling
• regime shift detection
• digital twins