Aiming at the current low efficiency of multi-physical field coupling simulation of electric equipment and the large error of the existing fast calculation method, a fast calculation method of electric-thermal coupling multi-physical field based on Deep Operator Network (DeepONet) is proposed. Taking 110 kV bushing as an example, Latin hypercubic sampling of finite element simulation is carried out to generate a data set, combined with multi-task DeepONet framework, and hyperparameter optimization is carried out by using Dream Optimization Algorithm (DOA) to realize high-precision and fast computation of the distribution of top flange stress, temperature, and displacement fields of the transformer bushing. This method only takes 0.005s for a single solution, and the accuracy of stress field, temperature field, and displacement field are 90.21%, 99.87%, and 99.09%, respectively; Compared to U-net and DNN proxy models, it has significantly improved in multiple evaluation metrics and robustness. Finally, the applicability of the model in real working conditions is verified by experiments. The model provides a reliable tool for digital twin scenarios such as power equipment structure optimization, state sensing, and multi-physical field reconstruction.