Prompting In-Context Operator Learning with Sensor Data, Equations, and Natural Language
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In the growing domain of scientific machine learning, in-context operator learning has demonstrated notable potential in learning operators from prompted data during inference stage without weight updates. However, the current model's overdependence on sensor 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. We propose the use of "captions" to integrate human knowledge about the operator, expressed through natural language descriptions and equations. We illustrate how this method not only broadens the flexibility and generality of physics-informed learning, but also significantly boosts learning performance and reduces data needs. Furthermore, we introduce a more efficient neural network architecture for multi-modal in-context operator learning, referred to as "ICON-LM", based on a language-model-like architecture. We demonstrate the viability of "ICON-LM" for scientific machine learning tasks, which creates a new path for the application of language models.
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