Graph In-Context Operator Networks for Generalizable Spatiotemporal Prediction

2026-03-13

AI Summary

This work addresses the limited generalization of traditional single-operator learning in spatiotemporal systems and its inability to leverage contextual examples for zero- or few-shot inference. To overcome these challenges, the authors propose GICON, a novel model that achieves geometric generalization through graph message passing and supports cardinality generalization via example-aware positional encoding, enabling inference of solution operators from contextual examples without updating model weights. As the first study to systematically compare contextual operator learning with classical approaches under identical training conditions, GICON establishes a unified framework integrating graph structure and contextual examples, demonstrating strong generalization across spatial domains and varying numbers of examples. Evaluated on air quality forecasting tasks in two regions of China, GICON significantly outperforms existing methods, delivering robust and accurate cross-domain spatiotemporal predictions from as few as a handful to over a hundred contextual examples.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• in-context operator learning
• classical operator learning
• spatiotemporal prediction
• generalization
• controlled comparison

Innovation

• in-context operator learning
• graph message passing
• example-aware positional encoding
• spatiotemporal prediction
• geometric generalization