# Chain of Operators: An Inference-Time Harness for In-Context Operator Learning

arXiv: https://arxiv.org/abs/2606.12318 · HTML: https://mlsanity.com/paper/2606.12318/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 50 references that are in the map.
- First posted on arXiv 10 Jun 2026.

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

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [A Survey on Large Language Model based Autonomous Agents](https://mlsanity.com/paper/2308.11432/) (2023)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [Augmented Language Models: a Survey](https://mlsanity.com/paper/2302.07842/) (2023)
- [LLM-Adapters: An Adapter Family for Parameter-Efficient Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2304.01933/) (2023)
- [Poseidon: Efficient Foundation Models for PDEs](https://mlsanity.com/paper/2405.19101/) (2024)
- [DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training](https://mlsanity.com/paper/2403.03542/) (2024)
- [Towards Foundation Models for Scientific Machine Learning: Characterizing Scaling and Transfer Behavior](https://mlsanity.com/paper/2306.00258/) (2023)
- [Physics-Informed Deep Neural Operator Networks](https://mlsanity.com/paper/2207.05748/) (2022)
- [In-Context Operator Learning with Data Prompts for Differential Equation Problems](https://mlsanity.com/paper/2304.07993/) (2023)
- [Deep transfer operator learning for partial differential equations under conditional shift](https://mlsanity.com/paper/2204.09810/) (2022)
- [Externalization in LLM Agents: A Unified Review of Memory, Skills, Protocols and Harness Engineering](https://mlsanity.com/paper/2604.08224/) (2026)
- [Reliable extrapolation of deep neural operators informed by physics or sparse observations](https://mlsanity.com/paper/2212.06347/) (2022)
- [Pretraining Codomain Attention Neural Operators for Solving Multiphysics PDEs](https://mlsanity.com/paper/2403.12553/) (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)
- [VICON: Vision In-Context Operator Networks for Multi-Physics Fluid Dynamics Prediction](https://mlsanity.com/paper/2411.16063/) (2024)
- [Zebra: In-Context Generative Pretraining for Solving Parametric PDEs](https://mlsanity.com/paper/2410.03437/) (2024)
- [LeMON: Learning to Learn Multi-Operator Networks](https://mlsanity.com/paper/2408.16168/) (2024)
- [DeepONet as a Multi-Operator Extrapolation Model: Distributed Pretraining with Physics-Informed Fine-Tuning](https://mlsanity.com/paper/2411.07239/) (2024)
- [In-Context Operator Learning on the Space of Probability Measures](https://mlsanity.com/paper/2601.09979/) (2026)
- [Probabilistic operator learning: generative modeling and uncertainty quantification for foundation models of differential equations](https://mlsanity.com/paper/2509.05186/) (2025)
- [In-Context Learning of Linear Systems: Generalization Theory and Applications to Operator Learning](https://mlsanity.com/paper/2409.12293/) (2024)
- [Solving Optimal Execution Problems via In-Context Operator Networks](https://mlsanity.com/paper/2501.15106/) (2025)
- [Graph In-Context Operator Networks for Generalizable Spatiotemporal Prediction](https://mlsanity.com/paper/2603.12725/) (2026)
- [Evolving Ensemble of Agents](https://mlsanity.com/paper/2605.09018/) (2026)
- [In-context modeling as a retrain-free paradigm for foundation models in computational science](https://mlsanity.com/paper/2604.23098/) (2026)

## Built on by (most cited first, 2 of 2)

- [A foundation model of numerical intelligence with cross-disciplinary generalization](https://mlsanity.com/paper/2607.28432/) (2026)
- [SeisEvo: Evolution of Seismic Data Reconstruction Algorithms by Agents](https://mlsanity.com/paper/2608.18272/) (2026)

## Abstract (arXiv)

While scientific foundation models show immense promise in accelerating physical simulations and numerical forecasting, they remain notoriously brittle when encountering out-of-distribution (OOD) scenarios. Adapting these generalist models to complex OOD tasks typically requires expensive parameter fine-tuning. In linguistic AI, this bottleneck is bypassed using "harnesses", which serve as external scaffolding such as reasoning chains and tool use to adapt frozen weights to complex tasks, yet designing an equivalent harness for physical domains remains an open frontier. To bridge this gap, we introduce Chain of Operators (CHOP), a framework that guides a frozen foundation model through complex OOD tasks without updating a single weight. By exploiting the in-context learning capability of In-Context Operator Networks (ICON), CHOP systematically decomposes unfamiliar problems into a sequence of explicit, closed-form mathematical operations and multiple model calls, translating OOD queries back into the model's learned operating regime. Across diverse benchmarks, including canonical PDE problems and real-world air-quality forecasting, CHOP consistently and substantially reduces inference errors compared to direct model evaluation. Crucially, these modular operator chains remain fully interpretable and can generalize across entirely distinct families of physical equations. Ultimately, this work demonstrates how frozen scientific models can adapt through programmable inference, establishing a modular, potential paradigm for agentic scientific computing.