The vulnerability of cities has increased with urbanization and climate change, making it more important to predict human mobility during extreme events (e.g., extreme weather) for downstream tasks including location-based early disaster warning and pre-allocating rescue resources, etc. However, existing human mobility prediction models are mainly designed for normal scenarios, and fail to adapt to extreme scenarios due to the shift of human mobility patterns under extreme scenarios. To address this issue, we introduce \textbf{X-MLM}, a cross-e\textbf{X}treme-event \textbf{M}obility \textbf{L}anguge \textbf{M}odel framework for extreme scenarios that can be integrated into existing deep mobility prediction methods by leveraging LLMs to model the mobility intention and transferring the common knowledge of how different extreme events affect mobility intentions between cities. This framework utilizes a RAG-Enhanced Intention Predictor to forecast the next intention, refines it with an LLM-based Intention Refiner, and then maps the intention to an exact location using an Intention-Modulated Location Predictor. Extensive experiments illustrate that X-MLM can achieve a 32.8\% improvement in terms of Acc@1 and a 35.0\% improvement in terms of the F1-score of predicting immobility compared to the baselines. The code is available at https://github.com/tsinghua-fib-lab/XMLM.

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