## 4 Conclusions  
In this study, a DNN is constructed with three hidden layers instead of the time-consuming fluid model to describe the CO\({}_{2}\) conversion in RF discharges at a given power density under Martian pressure involving tens of species and hundreds of reactions. A DNN that was well trained on the simulation data or experimental measurements was employed to describe the discharge characteristics and plasma chemistry of RF CO\({}_{2}\) discharges for various driving frequencies and power densities. The predicted results showed a good agreement with the fluid simulation results, and the MREs of various characteristics were less than 0.5%. It should be note that the qualified experimental data can also be applied to work as the training data; actually, the training dataset of a DNN only requires data of good quality and sufficient quantity, without concern regarding the source of the data. Usually, the fluid simulations solving the governing equations require nearly 20,000 s to  
Figure 14: Spatial distributions of the time-averaged (**a**) CO density and (**b**) O\({}_{2}\) density predicted by the DNN as a function of the power density at a given driving frequency of 13.56 MHz. Figure 15: The CO\({}_{2}\) conversion predicted by the DNN as a function of the power density at a given driving frequency of 13.56 MHz. obtain stable results on a given computational platform; however, after nearly two hours of training, the DNN only needed about 0.01 s to yield the key characteristics of the RF CO\({}_{2}\) discharge, such as the current-voltage characteristics, the electric field profiles, and the distribution of the particle densities. Compared to the traditional fluid model, the computational efficiency of the DNN was improved by about 10\({}^{6}\)-times, which indicates that the DNN could achieve almost real-time calculation of the CO\({}_{2}\) conversion in RF discharges with tens of species and hundreds of reactions. Due to the high computational efficiency, the DNN can provide a much larger amount of data than the traditional fluid model to enhance the simulation results, to show the spatial distributions of plasma species as a surface rather than as individual lines for various driving frequencies and input power densities, which vividly illustrate the evolution of the data and reveal more details about the underpinning physics. In addition, the DNN was applied to investigate the effects of the driving frequency and input power density on the CO\({}_{2}\) conversion in RF discharges. The predicted results also showed that, by increasing the driving frequency at a constant power density, an increase in the density of charged particles, neutral particles, and vibrationally excited CO\({}_{2}\) molecules can be observed; meanwhile, the CO\({}_{2}\) conversion also increases with the driving frequency. In addition, a slight improvement in CO\({}_{2}\) conversion was also observed as more power was coupled into the RF plasma. The study suggests that the DNN has an excellent ability to describe the discharge characteristics and plasma chemistry of RF CO\({}_{2}\) discharges with tens of species and hundreds of reactions. Data-driven models, such as DNNs, offer a promising approach to investigate plasma-based CO\({}_{2}\) conversion for various applications, which can be extended to more complex plasma modeling in future work. Software, R.L. ; Validation, R.L. and X.W. ; Investigation, X.W. ; Data curation, X.W. ; Writing--original draft, R.L. and X.W. ; Writing--review & editing, Y.Z. ; Project administration, Y.Z. ; Funding acquisition, Y.Z. All authors have read and agreed to the published version of the manuscript. This work was supported by the National Natural Science Foundation of China (No. 12375201). Not applicable. The data that support the findings of this study are available from the corresponding author upon reasonable request.