## 3 Results and Discussion  
Due to the high computational efficiency of the DNN, more simulation data can be calculated and the discharge characteristics can be predicted in detail in CO\({}_{2}\) discharges under Martian pressure at a given power density, which could allow discussing the effects of the driving frequency fairly on the RF discharges. In this section, the well-trained DNN is applied to predict the discharge characteristics and plasma chemistry of RF CO\({}_{2}\) discharges under Martian pressure for various driving frequencies at a given power density of 60 W/cm\({}^{2}\). Figure 6 shows the root-mean-squared (RMS) value of the current density and the RMS voltage as a function of the driving frequency at a fixed power density of 60 W/cm\({}^{2}\). When the driving frequency is increased from 12 to 75 MHz, the RMS current density is also increased from 58.5 to 114 mA/cm\({}^{2}\), almost two-fold growth, but at the same time, the RMS voltage is reduced from 317.5 V to 166.60 V, a decrease of about 1.91-times. The evolution of the current density and voltage at a given power density is consistent with the available experimental and simulation results [23; 30; 56], which further demonstrates the validation of the DNN constructed in the present study. Figure 7 plots the predictions for the spatial distributions of the time-averaged electric fields driven by the five different frequencies. After good training, the DNN can obtain the spatial profile of the electric field at any driving frequency in about 0.01 s. As shown in Figure 7, the maximum value of the electric field appears in the sheath region, that is at the electrode surface. According to the predicted data, the maximum electric field decreases from 3.78 to 2.25 kV/cm, partly because of the reduction in the applied voltage, and the thickness of the sheath region reduces from 184 to 105 um with the growth of the driving frequency from 13.56 to 67.8 MHz when the power density is fixed at 60 W/cm\({}^{2}\). This indicates that an increase in the driving frequency can effectively decrease the sheath electric field and compress the sheath region. Figure 6: RMS current density and RMS voltage predicted by the DNN as a function of the driving frequency at a given power density of 60 W/cm\({}^{2}\). Based on the prediction data, the predictions for the spatial profiles of the time-averaged electron density for various driving frequencies can be quickly obtained. From Figure 8, for a higher driving frequency, a larger electron density can be obtained with the maximum value located in the bulk plasma region. By altering the driving frequency from 13.56 to 67.8 MHz at a given power density of 60 W/cm\({}^{2}\), the maximum time-averaged electron density is also increased from \(1.31\times 10^{12}\) to \(2.75\times 10^{12}\) cm\({}^{-3}\), almost 2.1-fold growth. The increase in the electron density can be attributed to the enhancement of electron trapping with increasing driving frequency [57]. Then, the effect of the driving frequency on the electron temperature is shown in Figure 9, which gives the spatial distributions of the time-averaged electron density predicted by the DNN for various driving frequencies. As shown in Figure 9, the maximum electron temperature is achieved in the sheath region due to the acceleration of the sheath fields, and this maximum value decreases with the increase in frequency. The electron temperature in the sheath region decreases mainly for the reduction of the sheath electric field. Figure 8: Spatial distributions of the time-averaged electron density predicted by the DNN for various driving frequencies at a given power density of 60 W/cm\({}^{2}\). Figure 7: Spatial distributions of the time-averaged electric field predicted by the DNN for various driving frequencies at a given power density of 60 W/cm\({}^{2}\). In CO2 plasma, the vibrational energy in the vibrationally excited CO2 molecules can reduce the energy barrier of CO2 dissociation.