Liu Yang
Publications
Harness In-Context Operator Learning with Chain of Operators
Neural operators approximate mappings between function spaces, but often generalize poorly to other operators and usually require fine-tuning or retraining. In-Context Operator Networks (ICON) addresses this issue by prompting the model with numerical context so that the model learns specific operators from prompts and adapt to different operators without fine-tuning. However, ICON may still fail to generalize to out-of-distribution (OOD) operator tasks. Inpired by the success of harness engineering of Large Language models (LLMs), we introduce Chain of Operators (CHOP), a framework that harness a frozen ICON to OOD operator tasks without updating its parameters. Specifically, CHOP constructs a chain of operators consisting of explicit elementary transformations and the frozen ICON. Experiments on a scalar conservation law and a mean-field control problem show that CHOP reduces relative inference error over direct ICON evaluation, while each operator in the chain remains interpretable and in closed form. A chain constructed on one PDE family further generalizes to a different family, indicating shared mechanisms across harness systems.
Graph In-Context Operator Networks for Generalizable Spatiotemporal Prediction
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.