## 3 Results and Discussion
Based on tens of training datasets calculated from the fluid model, the DNN can yield nearly infinite prediction results in a given parameter range after good training, which greatly expands the parameter-traversal range of RF CO\({}_{2}\) discharge. Figure 12 provides the profiles of the CO\({}_{2}\) conversion versus the driving frequency at a given power density of 60 W/cm\({}^{2}\). A slight increase in CO\({}_{2}\) conversion with increasing driving frequency can be observed in Figure 12. According to the prediction results, the CO\({}_{2}\) conversion increases from 24.2% to 26.8% as the frequency changes from 12 MHz to 75 MHz. As the driving frequency increases, a considerable fraction of the energy is transferred from the electrons to the asymmetric stretching modes, increasing the density of the asymmetric stretching modes. The vibrational energy in the asymmetric stretching modes can lower the energy barrier of CO\({}_{2}\) decomposition; thus, the increase in the driving frequency enhances the rates of the electron impact reactions with vibrationally excited CO\({}_{2}\), leading to an improvement in CO\({}_{2}\) conversion. The input power has a significant impact on the CO\({}_{2}\) conversion in RF discharges under Martian pressure. Therefore, the well-trained DNN was employed to predict the effects of the input power on the discharge characteristics and plasma chemistry of RF CO\({}_{2}\) discharges from the perspective of the electric field, particle density, and CO\({}_{2}\) conversion. The predicted spatial distributions of the time-averaged electric field are given in Figure 13 using the well-trained DNN for various power densities at a driving frequency of 13.56 MHz. The electric field in the sheath region is significantly enhanced as more power is coupled to the RF plasmas. With the growth of the power density from 40 to 60 to 80 W/cm\({}^{2}\)  
Figure 12: The CO\({}_{2}\) conversion predicted by the DNN as a function of the driving frequency at a given power density of 60 W/cm\({}^{2}\). the maximum electric field increases monotonically from 3.15 to 3.79 to 4.28 kV/cm from the predicted data. In addition, the variation in the thickness of the sheath region can be neglected as the input power density varies. The strong sheath electric field is able to accelerate the electrons and improve the electron temperature. To gain insight into the variation of the neutral particles formed in CO\({}_{2}\) plasma as the power density varies, the spatial distributions of the time-averaged CO density and O\({}_{2}\) density as a function of the power density are predicted by the DNN in almost real time. From Figure 14a, the maximum CO density is \(1.57\times 10^{14}\) cm\({}^{-3}\) when the power density is \(35\ W/\)cm\({}^{2}\). As the power density is improved to \(85\ W/\)cm\({}^{2}\), the peak CO density reaches \(1.52\times 10^{15}\) cm\({}^{-3}\). The production of CO is mainly through electron impact dissociation processes. From the above analysis, more energetic electrons are produced with the growth of the power density, enhancing the rate of the dissociation process. As a result, a higher CO density can be achieved as the power density grows. Meanwhile, a similar evolutionary trend of O\({}_{2}\) density can be observed in Figure 14b. When the power density increases from 35 to 85 \(W/\)cm\({}^{2}\), the maximum time-averaged O\({}_{2}\) density rises from \(2.84\times 10^{13}\) to \(6.67\times 10^{13}\) cm\({}^{-3}\) based on the well-trained DNN. The primary reaction of producing O\({}_{2}\) is the ion reaction (\(\mathrm{e}+\mathrm{CO}_{2}^{+}\rightarrow\mathrm{C}+\mathrm{O}_{2}\)). Since the electron density and CO\({}_{2}^{+}\) density improve as the power density increases, then an increase in O\({}_{2}\) density can be observed in Figure 14b. The effect of the power density on CO\({}_{2}\) conversion is also described by using the well-trained DNN in this paper. Figure 15 gives the CO\({}_{2}\) conversion as a function of the power density at a given driving frequency of 13.56 MHz.