## 3 Results and Discussion
The effects of the driving frequency on the behaviors of the asymmetric stretching mode of CO2 molecules are also described by the well-trained DNN. Figure 10 gives the spatial profiles of the time-averaged densities of the asymmetric stretching mode of CO2 molecules predicted by the DNN as a function of driving frequency at a given power density of 60 W/cm2, where Figure 10a-h correspond to the spatial profiles of the time-averaged densities of CO2V1-CO2V8, respectively. As shown in Figure 10, the well-trained DNN can give the profiles of the asymmetric stretching mode of CO2 molecules with various driving frequencies as a surface, instead of individual lines. It can be seen that the densities of the asymmetric stretching modes increase monotonically with the driving frequency. In fact, the behaviors of the asymmetric stretching modes can be attributed to the competition between the electron impact vibrational excitation, VV relaxation, and vibration-translation (VT) relaxation [45]. When the power density is fixed as a constant, as the driving frequency increases, the characteristic time of VT relaxation increases, while the characteristic time of vibrational excitation and VV relaxation decreases, which explains why the density of asymmetric stretching modes increases with the driving frequency. Furthermore, as shown in Figure 10, it can be observed that the peak density of lower vibrational levels is closer to the electrode surface. In fact, the electron impact vibrational excitation and VV relaxation are the dominant reactions for the generation of asymmetric stretching modes. A considerable fraction of the lower vibrational energy levels are generated by electron impact vibrational excitation due to their lower threshold energy of vibrational excitation. In the sheath region, the strong electric field accelerates the electrons, resulting in a more efficient vibrational excitation process. Therefore, the maximum density of lower vibrational levels appears in the sheath region. Similarly, Figure 11 displays the prediction surfaces for the spatial distributions of the CO and O2 densities as a function of the driving frequency at a given power density of 60 W/cm2. According to the predicted data shown in Figure 11a, with the increase in the driving frequency from 12 to 75 MHz, the maximum CO density obtained in the bulk region increases from 7.02 \(\times\) 10\({}^{14}\) to 2.61 \(\times\) 10\({}^{15}\) cm\({}^{-3}\) by a factor of 3.72. In RF CO2 discharges under Martian pressure, the electron impact dissociation reaction (e + CO2 \(\rightarrow\) e + CO + O) is the main pathway to generate CO. As the frequency increases, although the electron temperature decreases, the increase in the electron density and vibrationally excited CO2 density still enhances the electron impact dissociation reaction with the excited-state CO2. As a result, the density of CO increases with the driving frequency. The predictions for the  
Figure 9: Spatial distributions of the time-averaged electron temperature predicted by the DNN for various driving frequencies at a given power density of 60 W/cm2. The well-trained DNN can give the behaviors of various species (such as charged species, neutral species, and excited species) formed in CO\({}_{2}\) plasma at different driving frequencies as a surface instead of separate lines. Similar prediction surfaces can be achieved using the DNN for the electric field and electron temperature. In other words, for RF CO\({}_{2}\) discharges driven at any frequency between 12 and 75 MHz, the DNN can obtain the corresponding discharge characteristics and plasma chemistry in 0.01 s with the same accuracy as the fluid simulation, which suggests that the essential characteristics of the CO\({}_{2}\) conversion in RF discharge under Martian pressure could be given in real time as the driving frequency changes.