## 2 Description of Methodology
### Validation of DNN  
Before the prediction of more data, the validation of the DNN should be performed, by comparing the predicted results obtained from the DNN with the simulation results calculated by the fluid model. The predicted results of the DNN are in good agreement with the fluid simulation results within the testing dataset, and the MREs for various discharge characteristics are less than 0.5%. To illustrate the good accuracy and high efficiency of the DNN, a comparison of the predicted discharge characteristics and plasma chemistry of RF CO\({}_{2}\) discharges at a frequency of 13.56 MHz and a power density of 60 W/cm\({}^{2}\) with the corresponding fluid simulation results is given. Figure 2 shows the predictions for the temporal evolutions of current density and voltage at a power density of 60 W/cm\({}^{2}\) and a driving frequency of 13.56 MHz, as well as the simulation results obtained from the fluid model. The solid and dashed lines in Figure 2 indicate the simulation and prediction results, respectively. It can be seen from the comparison in Figure 2 that the DNN yields very good predictions both in the current density and voltage domains, and the MREs for the current density and voltage are 0.18% and 0.42%, respectively. Figure 3 displays the spatial profiles of the time-averaged positive charge density, negative charge density, and electric field predicted by the DNN, together with the corresponding profiles simulated by the fluid model. As shown in Figure 3, the DNN predictions agree well with the simulation results, even in the sheath regions, where the electric field varies sharply. The MREs of positive charge density, negative charge density, and electric field in this case are 0.14%, 0.16%, and 0.41%, respectively. The bell-shaped spatial profiles for positive and negative charges are given in Figure 3 with the accumulation in the central region between electrodes, indicating that most charged particles are trapped in the bulk plasma region in RF discharge. In addition, the density of positi  
Figure 2: Temporal evolutions of current density and voltage predicted by the DNN in RF CO\({}_{2}\) discharge with a comparison of the results obtained from the fluid simulation. Red dotted line: the predicted current density; green dotted line: the predicted voltage. trodes is significantly higher than that of negative charges, leading to the formation of a space charge region accompanied by a stronger electric field. Then, the DNN predictions for the spatial distributions of product particle density are also compared with the simulation results. Figure 4 shows the spatial distributions of the time-averaged density of the charged particles predicted by the DNN at a power density of 60 W/cm\({}^{2}\) and a driving frequency of 13.56 MHz with the comparison of the simulation results obtained from the fluid model. Good agreement can be observed in Figure 4, and the MREs of the electron density, CO\({}_{2}^{+}\) density, O\({}_{2}^{+}\) density, O\({}^{-}\) density, and CO\({}_{3}^{-}\) density were also measured, which are 0.05%, 0.16%, 0.47%, 0.64%, and 0.16%, respectively. As illustrated in Figure 4, the density of the electrons is the highest among all the negative charges, reaching \(1.31\times 10^{12}\) cm\({}^{-3}\) in the bulk plasma region. The densities of the O\({}^{-}\) and CO\({}_{3}^{-}\) ions are an order of magnitude lower than that of electrons. The CO\({}_{2}^{+}\) ions are the dominant positive charge with a maximum density of \(1.26\times 10^{12}\) cm\({}^{-3}\), followed by the O\({}_{2}^{+}\) ions with a maximum density of \(4.73\times 10^{11}\) cm\({}^{-3}\). The vibrationally excited CO\({}_{2}\) is considered to play a key role in the splitting of CO\({}_{2}\) under Martian pressure. Figure 5 plots the spatial distributions of the time-average vibrationally excited CO\({}_{2}\) density predicted by the DNN, together with the simulation results obtained from the fluid model.