mlsanityData to 7 Oct 2026

Graph In-Context Operator Networks for Generalizable Spatiotemporal Prediction

arXiv 2603.12725 ↗First posted 13 Mar 2026cs.LG cs.AIcited by 3

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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.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 38 of its 55 references that are in the map. First posted on arXiv 13 Mar 2026.

Builds on

38 of 55 references.

References · 38

  1. 2020Language Models are Few-Shot Learnerscited by 32,199
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  3. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  4. 2019Root Mean Square Layer Normalizationcited by 1,425
  5. 2020Learning to Simulate Complex Physics with Graph Networkscited by 867
  6. 2020Learning Mesh-Based Simulation with Graph Networkscited by 840
  7. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 722
  8. 2017DGM: A deep learning algorithm for solving partial differential equationscited by 674
  9. 2017The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problemscited by 581
  10. 2017Solving high-dimensional partial differential equations using deep learningcited by 549
  11. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 537
  12. 2024The Faiss librarycited by 370
26 more
  1. 2022Message Passing Neural PDE Solverscited by 368
  2. 2020Multipole Graph Neural Operator for Parametric Partial Differential Equationscited by 343
  3. 2023GNOT: A General Neural Operator Transformer for Operator Learningcited by 321
  4. 2017PDE-Net: Learning PDEs from Datacited by 304
  5. 2023Geometry-Informed Neural Operator for Large-Scale 3D PDEscited by 293
  6. 2021U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flowcited by 292
  7. 2017Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equationscited by 188
  8. 2022FourCastNet: Accelerating Global High-Resolution Weather Forecasting using Adaptive Fourier Neural Operatorscited by 188
  9. 2024Poseidon: Efficient Foundation Models for PDEscited by 186
  10. 2022MIONet: Learning multiple-input operators via tensor productcited by 180
  11. 2023In-Context Operator Learning with Data Prompts for Differential Equation Problemscited by 98
  12. 2023Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestrationcited by 46
  13. 2024PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamicscited by 33
  14. 2024Data-Efficient Operator Learning via Unsupervised Pretraining and In-Context Learningcited by 32
  15. 2024PDE Generalization of In-Context Operator Networks: A Study on 1D Scalar Nonlinear Conservation Lawscited by 30
  16. 2024Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networkscited by 28
  17. 2024VICON: Vision In-Context Operator Networks for Multi-Physics Fluid Dynamics Predictioncited by 22
  18. 2025RIGNO: A Graph-based framework for robust and accurate operator learning for PDEs on arbitrary domainscited by 22
  19. 2023D2NO: Efficient Handling of Heterogeneous Input Function Spaces with Distributed Deep Neural Operatorscited by 18
  20. 2023PROSE: Predicting Operators and Symbolic Expressions using Multimodal Transformerscited by 16
  21. 2024Zebra: In-Context Generative Pretraining for Solving Parametric PDEscited by 14
  22. 2025Probabilistic operator learning: generative modeling and uncertainty quantification for foundation models of differential equationscited by 9
  23. 2026In-Context Operator Learning on the Space of Probability Measurescited by 7
  24. 2025PCDCNet: A Surrogate Model for Air Quality Forecasting with Physical-Chemical Dynamics and Constraintscited by 5
  25. 2025Solving Optimal Execution Problems via In-Context Operator Networkscited by 4
  26. 2025Continuum Transformers Perform In-Context Learning by Operator Gradient Descentcited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026Evolving Ensemble of Agentscited by 2
  2. 2026Chain of Operators: An Inference-Time Harness for In-Context Operator Learningcited by 2
  3. 2026A foundation model of numerical intelligence with cross-disciplinary generalizationcited by 0