Dielectric elastomer actuators (DEAs) enable to create soft robots with fast response speed and high-energy density, but the fast optimization design of DEAs still remains elusive because of their continuous electromechanical deformation and high-dimensional design space. Existing approaches usually involve repeating and vast finite element calculation during the optimization process, leading to low efficiency and time consuming. The advance of deep learning has shown the potential to accelerate the optimization process, but the high-dimensional design space leads to challenge on the accuracy and generality of the deep learning model. In this work, we propose a deep learning-based automatic design framework for DEAs, capable of rapidly generating high-dimensional distributed electrode patterns based on different design objects. This framework is developed as follows: (1) a dataset construction strategy combining with a finite element model is developed to optimize the data distribution within the high-dimensional design space; (2) a neural network-embedded physical information is designed and trained to achieve accurate prediction of the continuous deformation within 0.011s; and (3) a genetic algorithm with the neural network is proposed to automatically and rapidly optimize the electrode pattern of DEAs based on various design objects. To verify the effectiveness, a series of case studies (including maximum displacement, specific displacement, multiplicity of solutions, multiple degree-of-freedom actuations, and complex actuations) has been conducted. Both simulation results and experimental data demonstrate that our design framework can automatically design the electrode pattern within 2 min and obviously improve the performance of DEAs. This work proposes a deep learning-based design approach with automatic and rapid property, thereby paving the way for broader applications of DEAs.