In the growing domain of scientific machine learning, in-context operator learning has shown notable potential in learning operators and solving differential equations using prompted data, during the inference stage without weight updates. However, the current model's overdependence on function data, may inadvertently overlook the invaluable human insight into the operator. To address this, we present a transformation of in-context operator learning into a multi-modal paradigm. In particular, we take inspiration from the recent success of large language models, and propose using "captions" to integrate human knowledge about the operator, expressed through natural language descriptions and equations. Also, we introduce a novel approach to train a language-model-like architecture, or directly fine-tune existing language models, for in-context operator learning. We beat the baseline on single-modal learning tasks, and also demonstrated the effectiveness of multi-modal learning in enhancing performance and reducing function data requirements. The proposed method not only significantly improves in-context operator learning, but also creates a new path for the application of language models.

翻译：在科学机器学习这一日益发展的领域中，上下文内算子学习已展现出显著潜力，能在推理阶段利用提示数据学习算子并求解微分方程，而无需更新权重。然而，当前模型对函数数据的过度依赖，可能无意中忽视了人类对算子的宝贵洞察。为解决这一问题，我们将上下文内算子学习转化为一种多模态范式。具体而言，受大语言模型近期成功的启发，我们提出使用“标题”来整合关于算子的人类知识，通过自然语言描述与方程表达。同时，我们引入了一种新颖方法，用于训练类似语言模型的架构，或直接微调现有语言模型，以实现上下文内算子学习。我们在单模态学习任务上超越了基线，并展示了多模态学习在提升性能及减少函数数据需求方面的有效性。所提出的方法不仅显著改进了上下文内算子学习，还为语言模型的应用开辟了新途径。