Fig. 2: Overview of long-term prediction results for dynamic systems.

a Illustration of dynamic systems represented as graph and grid structures. b Hybrid training method to enable the model’s applicability to different graph structures. c Mask training approach designed for adapting the model to various grid structures. d The prediction task in the graph structure focuses on the response of train nodes in the y and z directions within a train-bridge coupled system under seismic action. Nodes 1 to 4 corresponding to the 1st to 4th carriages respectively, feature 1–4 represent the acceleration of the carriage in the y and z direction. e Global monthly average temperature prediction, corresponding to the prediction task in a grid structure.