# Graph In-Context Operator Networks for Generalizable Spatiotemporal Prediction

arXiv: https://arxiv.org/abs/2603.12725 · HTML: https://mlsanity.com/paper/2603.12725/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 55 references that are in the map.
- First posted on arXiv 13 Mar 2026.

## Builds on (most cited first, 30 of 38)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems](https://mlsanity.com/paper/1710.00211/) (2017)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [The Faiss library](https://mlsanity.com/paper/2401.08281/) (2024)
- [Multipole Graph Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2006.09535/) (2020)
- [GNOT: A General Neural Operator Transformer for Operator Learning](https://mlsanity.com/paper/2302.14376/) (2023)
- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [Poseidon: Efficient Foundation Models for PDEs](https://mlsanity.com/paper/2405.19101/) (2024)
- [Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations](https://mlsanity.com/paper/1706.04702/) (2017)
- [FourCastNet: Accelerating Global High-Resolution Weather Forecasting using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2208.05419/) (2022)
- [MIONet: Learning multiple-input operators via tensor product](https://mlsanity.com/paper/2202.06137/) (2022)
- [In-Context Operator Learning with Data Prompts for Differential Equation Problems](https://mlsanity.com/paper/2304.07993/) (2023)
- [Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestration](https://mlsanity.com/paper/2303.04778/) (2023)
- [PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics](https://mlsanity.com/paper/2409.09811/) (2024)
- [Data-Efficient Operator Learning via Unsupervised Pretraining and In-Context Learning](https://mlsanity.com/paper/2402.15734/) (2024)
- [PDE Generalization of In-Context Operator Networks: A Study on 1D Scalar Nonlinear Conservation Laws](https://mlsanity.com/paper/2401.07364/) (2024)
- [Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networks](https://mlsanity.com/paper/2402.15406/) (2024)
- [VICON: Vision In-Context Operator Networks for Multi-Physics Fluid Dynamics Prediction](https://mlsanity.com/paper/2411.16063/) (2024)
- [RIGNO: A Graph-based framework for robust and accurate operator learning for PDEs on arbitrary domains](https://mlsanity.com/paper/2501.19205/) (2025)

## Built on by (most cited first, 3 of 3)

- [Evolving Ensemble of Agents](https://mlsanity.com/paper/2605.09018/) (2026)
- [Chain of Operators: An Inference-Time Harness for In-Context Operator Learning](https://mlsanity.com/paper/2606.12318/) (2026)
- [A foundation model of numerical intelligence with cross-disciplinary generalization](https://mlsanity.com/paper/2607.28432/) (2026)

## Abstract (arXiv)

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.