Nonlinear mapping of the fuzzy relation exists between structural inputs and outputs, as well as between structural global and local response. It is difficult for the numerical simulation to introduce the nonlinear effects of the variability of loading effects and the uneven deterioration of structure. The big monitoring data make it feasible to mine these nonlinear effects, and the network of deep learning is a good tool to establish the nonlinear mapping model between the multi-source monitoring data. Based on the temperature, strain, and dynamic displacement data from the structural health monitoring (SHM) system of an in-service bridge, the deep learning regression network of long short-term memory (LSTM) is designed and trained, which is used for modeling the nonlinear mapping between the structural input-output and the structural global-local response. The digital model of the nonlinear mapping of the temperature to temperature-induced strain, dynamic displacement to vehicleinduced strain, and vehicle-induced strain to dynamic displacement is established by the deep learning of LSTM regression network. The established nonlinear mapping model can be used to recover the abnormal and missing data with multi-source data, and it digitally linked the structural input-output and the structural global-local response. Then, the utilization of SHM data analytics will be enhanced, and the digital modeling for the in-service state of the bridge structure will be fast implemented.