Title: APIC: Amortized Physics-Informed Calibration using Neural Processes

Abstract: Physics-based models frequently suffer from inherent inaccuracies stemming from incomplete or incorrectly specified mechanisms, which creates a persistent gap between theoretical predictions and empirical data. While the Kennedy-O'Hagan (KOH) framework attempts to resolve these systematic errors through explicit discrepancy modeling, its traditional per-instance approach lacks the scalability required for families of related systems. To overcome this limitation, we present Amortized Physics-Informed Calibration (APIC), a population-level generalization of KOH that utilizes Neural Processes to facilitate scalable Bayesian inference across multiple realizations. APIC adopts a two-branch latent structure designed to separate instance-specific physical parameters from shared, state-dependent structural discrepancies. By embedding differentiable physics within an amortized inference backbone, the framework allows for the swift calibration of previously unseen systems using only sparse data, all while providing robust uncertainty quantification. Our evaluations, conducted on the damped spring oscillator, the Lotka-Volterra system, and an advection-diffusion partial differential equation featuring misspecified physics, reveal that APIC achieves superior parameter recovery and more consistent identification of systemic discrepancy structures than existing calibration methods.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC