AI summaryⓘ
The authors point out that physics models often don't perfectly match real-world data because they miss some parts or details. They build on an existing method called Kennedy-O'Hagan to fix these mismatches, but make it work better across many similar systems by using a machine learning approach called Neural Processes. Their new method, APIC, separates specific differences for each case from common, shared errors and can quickly adjust models for new situations while also showing how sure it is about those adjustments. They tested their method on several example systems and found it does a better job at fixing parameters and spotting errors than other methods. This helps make physics models more accurate and reliable when applied to different but related problems.
Physics-informed modelingKennedy-O'Hagan frameworkAmortized inferenceNeural ProcessesBayesian calibrationSystematic discrepancyParameter recoveryDamped spring oscillatorLotka-Volterra systemAdvection-diffusion PDE
Authors
Aishwarya Venkataramanan, Sai Karthikeya Vemuri, Joachim Denzler
Abstract
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.