## 2 Description of Methodology  
### Description of Fluid Model  
In this paper, the RF CO\({}_{2}\) discharge is ignited between two parallel plate electrodes with an electrode spacing of 2 mm, and the electrode gap is filled with CO\({}_{2}\) gas at a Martian pressure of 4.5 Torr. Based on Martian conditions, 26 species were selected using a zero-dimensional kinetic model [44]. These plasma species in this model include seven charged species (electron, O\({}^{-}\), O\({}_{2}^{-}\), CO\({}_{3}^{-}\), CO\({}_{4}^{-}\), CO\({}_{2}^{+}\), and O\({}_{2}^{+}\)), five neutral species (CO, C, O, O\({}_{2}\), and O\({}_{3}\)), 13 excited species (CO\({}_{2}\)e\({}_{1}\), CO\({}_{2}\)v\({}_{a}\), CO\({}_{2}\)v\({}_{b}\), CO\({}_{2}\)v\({}_{c}\), CO\({}_{2}\)v\({}_{1a}\), CO\({}_{2}\)v\({}_{1}\), CO\({}_{2}\)v\({}_{2}\), CO\({}_{2}\)v\({}_{3}\), CO\({}_{2}\)v\({}_{4}\), CO\({}_{2}\)v\({}_{5}\), CO\({}_{2}\)v\({}_{6}\), CO\({}_{2}\)v\({}_{7}\), and CO\({}_{2}\)v\({}_{8}\)), and the dominant background gas CO\({}_{2}\). The chemical reactions in CO\({}_{2}\) plasma and the corresponding reaction coefficients were obtained from the previous study in Ref. [44]. The simulation results obtained from the fluid model were used as the data source for training the DNN, and the effectiveness of this fluid model was verified in Ref. [45] by comparing with the experimental measurements. The governing equations in this fluid model include the continuity equations with drift-diffusion approximation, the Poisson equation, and the electron energy conservation equation as follows [46; 47; 48]:  
\[\frac{\partial n_{i}}{\partial t}+\frac{\partial I_{i}}{\partial x}=R_{i} \tag{1}\]  
\[\Gamma_{i}=q_{i}\mu_{i}n_{i}E-D_{i}\frac{\partial n_{i}}{\partial x} \tag{2}\]  
\[\frac{\partial E}{\partial x}=\frac{\rho}{\varepsilon_{0}} \tag{3}\]  
\[\frac{\partial}{\partial t}\bigg{(}\frac{3}{2}k_{\text{B}}n_{\text{e}}T_{ \text{e}}\bigg{)}=-\frac{\partial Q_{\text{e}}}{\partial x}-e_{0}\sum_{j} \Delta Ej_{j}-e_{0}\Gamma_{\text{e}}E-3k_{\text{B}}n_{\text{e}}\frac{m_{ \text{e}}}{m_{\text{gas}}}\big{(}T_{\text{e}}-T_{\text{gas}}\big{)}\overline{ v_{\text{e}}} \tag{4}\]  
where \(n_{i}\), \(\Gamma_{i}\), and \(R_{i}\) are the number density, flux, and generation/destruction rate for species with index label \(i\), respectively. \(q_{i}\), \(\mu_{i}\), and \(D_{i}\) are the charge number (e.g., \(+1\) for a CO\({}_{2}^{+}\) ion), the mobility, and the diffusion coefficient for species \(i\), respectively. \(E\), \(\rho\), \(\varepsilon_{0}\), \(k_{\text{B}}\), \(Q_{\text{e}}\), \(e_{0}\), \(\Delta E_{j}\), \(k_{j}\), \(\overline{v_{\text{e}}}\), \(m_{\text{e}}\), \(m_{\text{gas}}\), \(T_{\text{e}}\), and \(T_{\text{gas}}\) are the electric field, space charge density, vacuum permittivity, Boltzmann constant, electron thermal flux, elementary charge, energy lost per electron in an inelastic collision reaction \(j\), rate coefficient of reaction \(j\), electron momentum transfer collision frequency with the background gas, electron mass, gas species mass, electron temperature, and gas temperature, respectively. The flux boundary conditions for all species and electron energy are considered at the surface of the electrodes, and for the boundary conditions of the electrons, the secondary electron emission is also considered [49]. In addition, the surface reactions are considered at the boundary of the discharge gap [50]. A sinusoidal voltage expressed as \(V(t)=V_{0}\text{sin}(2\pi ft)\) is taken as the input parameter, where \(V_{0}\) is the amplitude of the voltage and \(f\) is the driving frequency. In order to avoid the disturbance of other discharge parameters, the effect of the driving frequency on CO\({}_{2}\) conversion in RF discharge should be investigated at a constant power density. For a given power density P\({}_{0}\), the corresponding applied voltage is calculated as \(V_{0}^{(l+1)}=V_{0}^{(l)}+\alpha\Big{(}P_{0}-P^{(l)}\Big{)}\), where \(\alpha\) is a tiny constant to optimize the approach speed and \(P\) is the given power density.