It seems that there is one work that applied LLM to abstract interpretation:
Can LLMs Formally Reason as Abstract Interpreters for Program Analysis?
Authors: Jacqueline L. Mitchell, Brian Hyeongseok Kim, Chenyu Zhou, Chao Wang
Link: https://arxiv.org/pdf/2503.12686
Although there is only one work on LLM for abstract interpretation, I think that it can be a research direction (there might be more papers in the future).
Please kindly review.