APIC: Amortized Physics-Informed Calibration using Neural Processes

Aishwarya Venkataramanan, Sai Karthikeya Vemuri, Joachim Denzler
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:6900-6916, 2026.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-venkataramanan26a, title = {{APIC}: Amortized Physics-Informed Calibration using Neural Processes}, author = {Venkataramanan, Aishwarya and Vemuri, Sai Karthikeya and Denzler, Joachim}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {6900--6916}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/venkataramanan26a/venkataramanan26a.pdf}, url = {https://proceedings.mlr.press/v337/venkataramanan26a.html}, 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.} }
Endnote
%0 Conference Paper %T APIC: Amortized Physics-Informed Calibration using Neural Processes %A Aishwarya Venkataramanan %A Sai Karthikeya Vemuri %A Joachim Denzler %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-venkataramanan26a %I PMLR %P 6900--6916 %U https://proceedings.mlr.press/v337/venkataramanan26a.html %V 337 %X 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.
APA
Venkataramanan, A., Vemuri, S.K. & Denzler, J.. (2026). APIC: Amortized Physics-Informed Calibration using Neural Processes. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:6900-6916 Available from https://proceedings.mlr.press/v337/venkataramanan26a.html.

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