This repository contains the official implementation for the paper "APIC: Amortized Physics-Informed Calibration using Neural Processes".

APIC expands the classical Kennedy-O'Hagan (KOH) framework by incorporating an amortized inference backbone to rapidly calibrate physical parameters and identify state-dependent structural discrepancies across a collection of related physics systems.

APIC utilizes a dual-latent architecture to decouple system parameters $\theta$ from unmodeled structural physics $c$. This repository contains the implementation for the 1D Advection-Diffusion-Reaction PDE system for three different Neural Process backbones:

• APIC-CNP: Conditional Neural Process with deterministic mean aggregation.
• APIC-LNP: Latent Neural Process incorporating stochastic variational latent variables.
• APIC-ANP: Attentive Neural Process using target-dependent cross-attention.

1. Installation

git clone https://github.com/cvjena/APIC.git
cd APIC
pip install -r requirements.txt

2. Training a model

You can run experiments using main.py. By default, running the script trains the APIC-ANP backbone model:

python main.py --model_type ANP --steps_p1 2000 --steps_p2 4000

The training loop proceeds in two stages:

Phase 1 (Nominal Pre-training): Learns inverse parameter estimation mappings purely on nominal datasets where $c = 0$.

Phase 2 (Joint Discrepancy Calibration): Calibrates parameters alongside a learned variance head under hidden physical discrepancies.

If you use this code or framework, please consider citing our work:

@article{venkataramanan2026apic,
  title={APIC: Amortized Physics-Informed Calibration using Neural Processes},
  author={Venkataramanan, Aishwarya and Vemuri, Sai Karthikeya and Denzler, Joachim},
  journal={arXiv preprint arXiv:2606.03355},
  year={2026}
}