Abstract: Amid the accelerating transformation of the global energy structure, hydrogen energy, with its characteristics of abundant resources and zero carbon emissions, has emerged as a crucial part of China's energy development strategy. Underground salt cavern hydrogen storage has significant advantages in terms of cost, scale, and storage cycle. However, currently there are relatively few construction and operation cases in China, and the intelligent evaluation of the stability of salt cavern hydrogen storage facilities only considers data-driven approaches, without exploring the impact of physical information constraints. This paper proposes a generative model framework based on Transformer for the stability evaluation of salt cavern hydrogen storage facilities. For the generative model of the stability evaluation of salt cavern hydrogen storage facilities, a multi-scenario database of real data + virtual data is constructed. A generative model training and state adaptive optimization method based on data-driven and mechanism constraints is established. A hierarchical early warning system for the stability evaluation of salt cavern hydrogen storage is proposed, and an intelligent early warning platform based on the "edge - cloud collaboration" double-layer architecture is developed. Comprehensively, two methods-field observation comparison and scenario simulation early warning response-are used for application verification, which can provide technical support for the stability evaluation of salt cavern hydrogen storage facilities under different operating conditions.