Graph In-Context Operator Networks for Generalizable Spatiotemporal Prediction

TL;DR

This paper introduces GICON, a graph-based in-context operator learning model that outperforms classical models in spatiotemporal prediction tasks, demonstrating strong generalization and scalability.

Contribution

It systematically compares in-context operator learning with classical methods and proposes GICON, combining graph message passing and positional encoding for improved generalization.

Findings

In-context operator learning outperforms classical models on air quality prediction.

GICON generalizes across spatial domains and scales from few to many training examples.

Experiments show robust performance on real-world spatiotemporal data.

Abstract

In-context operator learning enables neural networks to infer solution operators from contextual examples without weight updates. While prior work has demonstrated the effectiveness of this paradigm in leveraging vast datasets, a systematic comparison against single-operator learning using identical training data has been absent. We address this gap through controlled experiments comparing in-context operator learning against classical operator learning (single-operator models trained without contextual examples), under the same training steps and dataset. To enable this investigation on real-world spatiotemporal systems, we propose GICON (Graph In-Context Operator Network), combining graph message passing for geometric generalization with example-aware positional encoding for cardinality generalization. Experiments on air quality prediction across two Chinese regions show that in-context operator learning outperforms classical operator learning on complex tasks, generalizing across spatial domains and scaling robustly from few training examples to 100 at inference.