Fine-Tune Language Models as Multi-Modal Differential Equation Solvers

In the growing domain of scientific machine learning, in-context operator learning has shown notable potential in building foundation models, as in this framework the model is trained to learn operators and solve differential equations using prompted data, during the inference stage without weight updates. However, the current model's overdependence on function data overlooks 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 …

building context cs.lg cs.na current data differential differential equation domain equation foundation framework function inference language language models learn machine machine learning math.na modal multi-modal operators solve stage stat.ml updates