APIC: Amortized Physics-Informed Calibration using Neural Processes
For practitioners needing to calibrate physics models across many related systems, APIC provides a scalable, amortized alternative to per-instance calibration.
APIC extends the Kennedy-O'Hagan calibration framework to population-level inference using Neural Processes, enabling rapid calibration of unseen physical systems from sparse observations while quantifying uncertainty. Experiments on three benchmark systems show improved parameter recovery and consistent discrepancy identification compared to existing methods.
Physics models are inherently imperfect due to misspecified or missing mechanisms, resulting in systematic discrepancies between model predictions and real-world observations. The Kennedy-O'Hagan (KOH) framework addresses this issue through explicit discrepancy modeling. However, its non-amortized, per-instance formulation limits scalability across families of related systems. We introduce Amortized Physics-Informed Calibration (APIC), a population-level extension of KOH that leverages Neural Processes to perform scalable Bayesian inference across realizations. Our framework employs a two-branch latent architecture to disentangle instance-specific physical parameters from shared, state-dependent structural discrepancies. By integrating differentiable physics into an amortized inference backbone, APIC enables rapid calibration of unseen realizations from sparse observations while quantifying uncertainty. Experiments on the damped spring oscillator, the Lotka-Volterra system, and the advection-diffusion PDE with misspecified physics demonstrate improved parameter recovery and consistent identification of the systemic discrepancy structure compared to other calibration approaches.