APIC: Amortized Physics-Informed Calibration using Neural Processes

We introduce a semi-parametric framework for nonlinear system identification, which decouples discrepancy functions from physics-based components. Orthogonal Gaussian process regression balances sparse parameter selection (the white box) with discrepancy learning (the black box) to produce interpretable models from incomplete physics.

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.

Calibration remains one of the principal obstacles to the deployment of machine learning in scientific instrumentation because it typically relies on expert intervention, dedicated procedures, and manually labelled data. We introduce a physics-informed self-supervised framework that jointly learns latent detector calibration parameters and task-specific predictions directly from raw measurements without requiring pre-calibrated signals or external labels. The method exploits known physical constraints to generate pseudo-labels iteratively, transforming calibration into a self-supervised optimization problem. The approach is demonstrated for ionic charge-state determination in the VAMOS++ magnetic spectrometer, where the calibration of a segmented ionization chamber and the inference of ionic charge states are learned simultaneously. Starting from a weak prior on the mean ionic charge state, the model progressively refines its predictions through iterative fractional pseudo-labelling driven by the discrete nature of atomic masses. Beyond accurate ionic charge-state reconstruction, the inferred calibration coefficients provide a compact representation of the detector state that enables automated monitoring of gain drifts, pressure variations, and detector aging. The resulting labels can subsequently be transferred to specialized models that quantify detector imperfections and track their spatial and temporal evolution. These results establish a general paradigm for self-calibrating and self-monitoring scientific instruments and represent a step toward intelligent experimental systems capable of autonomous calibration, analysis, and performance optimization.