This paper presents an in-depth examination of the nonlinear deformation induced by dielectric actuation in pre-stressed ideal dielectric elastomers. A nonlinear ordinary differential equation that governs this deformation is formulated based on the hyperelastic model under dielectric stress. By means of numerical integration and neural network approximations, the relationship between voltage and stretch is established. Neural networks are utilized to approximate solutions for voltage-to-stretch and stretch-to-voltage transformations obtained via an explicit Runge-Kutta method. The efficacy of these approximations is illustrated by their use in compensating for nonlinearity through the waveshaping of the input signal. The comparative analysis demonstrates that the approximated solutions are more accurate than baseline methods, resulting in reduced harmonic distortions when dielectric elastomers are used as acoustic actuators. This study highlights the effectiveness of the proposed approach in mitigating nonlinearities and enhancing the performance of dielectric elastomers in acoustic actuation applications.