Machine learning-driven optimization of plasma-coupled photocatalytic CO₂ reduction system for syngas production

Experimental equipment, processes and photocatalyst preparation

Detailed information on the experimental equipment, experimental procedures and photocatalyst preparation is provided in the Supplementary Materials.

The procedures of the machine learning

The P²CR system, as illustrated in Supplementary Figure 1, is influenced by many factors, including discharge power, catalyst dosage, gas flow rate, humidity, and light intensity. These five variables were selected because they were experimentally varied in all 120 runs and represent the main operation-level descriptors of the present plasma-coupled photocatalytic reactor. Discharge power controls the plasma energy input, catalyst dosage determines the amount of available catalytic surface, gas flow rate affects reactant throughput and residence time, relative humidity regulates water participation and the plasma reaction atmosphere, and light intensity governs photocatalyst excitation. These variables were therefore selected as the most relevant operating parameters for model construction and optimization within the present fixed catalyst-reactor system. Other potentially influential factors, including catalyst composition, reactor geometry, electrode gap, plasma frequency, and the CO₂/Ar feed ratio, were kept constant in the present study and were not included as input variables. This design was adopted because the objective was to optimize the operating conditions of a fixed Cu-Pd/TiO₂ plasma-coupled photocatalytic system rather than to compare different catalysts or reactor configurations. In addition, the dataset contained 120 experimental runs. Introducing additional material-level and reactor-level variables would have increased the dimensionality of the problem and reduced the interpretability and statistical robustness of the small-sample machine-learning analysis.

Figure 1 illustrates the workflow of model construction, training, optimization, and evaluation in this study. The machine-learning workflow was designed to avoid information leakage during model development. The dataset consisted of 120 experimental samples and was divided by the Sample set Partitioning based on joint X-Y distances (SPXY) algorithm into a training set (n = 96) and an external test set (n = 24). The training set was used for model development and parameter optimization, whereas the external test set was used for final performance evaluation and subsequent permutation feature importance (PFI) analysis. Five experimentally measured operating variables, namely discharge power, catalyst dosage, gas flow rate, relative humidity, and light intensity, were used as the primary input features. To capture nonlinear interactions, nine engineered features were additionally constructed: power/flow, dosage/flow, light intensity/flow, humidity × light intensity, power × light intensity, humidity × flow, 1/flow, power/dosage, and dosage × light intensity. The hybrid model used five experimentally controllable variables together with nine engineered descriptors for nonlinear feature representation. For the Kernel Ridge Regression (KRR) model, the input features were standardized using StandardScaler within the modeling pipeline. The tree-based Gradient Boosting Regressor (GBR) model was fitted directly to the raw and engineered input features without feature standardization. No target transformation or target normalization was applied during model fitting; all predictions and evaluation metrics were calculated in the original physical units. During SPXY splitting, the input and output variables were temporarily standardized only for calculating distances in the combined X-Y space. This temporary scaling was not used to transform the model targets. In addition, mean squared error (MSE) was used during hybrid-weight selection. Five repeated five-fold cross-validation was used to screen the candidate base learners. Hyperparameter optimization was performed using four-fold inner cross-validation within the training set only. The optimized GBR parameters were n_estimators = 280, learning rate = 0.06, max depth = 2, subsample = 0.85, and min samples leaf = 1. The optimized KRR parameters were alpha = 0.06 and gamma = 0.10 with an Radial Basis Function (RBF) kernel. After fixing the base-model hyperparameters, the shared hybrid weight was optimized using three-fold out-of-fold predictions generated only from the training set. The weight-search step size was 0.01. The random seeds were fixed at 42 for hyperparameter cross-validation and 2026 for the inner out-of-fold hybrid-weight optimization and GBR training. The repeated cross-validation seeds were also fixed in advance. All analyses were performed in Python 3.11.15 using NumPy 2.4.6, pandas 3.0.5, SciPy 1.17.1, scikit-learn 1.9.0, and joblib 1.5.3.

Figure 1. Process scheme of the optimization, evaluation and prediction framework for the hybrid machine-learning model. RMSE: Root mean square error; MAE: mean absolute error; MSE: mean squared error; SPXY: sample set partitioning based on joint X-Y distances; GBR: gradient boosting regressor; KRR: kernel ridge regression.

Description of the hybrid model

A single machine learning model may be sensitive to local data structures, noise, or train-test splitting^[27-29]. To address these challenges, we developed a hybrid model with shared weights by combining GBR and KRR. GBR is a tree-based ensemble method capable of capturing nonlinear relationships, local threshold effects, and interactions between variables^[30]. In contrast, KRR performs smooth kernel-based regression and is suitable for modeling continuous nonlinear responses in small-sample datasets^[31]. These two models have different learning mechanisms: GBR focuses on local nonlinear partitioning of the feature space, whereas KRR describes global smooth nonlinear trends based on kernel similarity. Their complementary characteristics motivated the construction of the hybrid model. The hybrid prediction was defined as:

where P_GBR and P_KRR are the predictions of GBR and KRR, respectively, and W represents the weight assigned to GBR. Within the SPXY training set, cross-validation was used to generate out-of-fold predictions from GBR and KRR^[32]. The hybrid weight W was then searched from 0 to 1 with a step size of 0.01. For each candidate weight, the hybrid prediction was calculated and evaluated by the mean squared error^[33]:

where $$ y_{j}^{pred} $$ is the predicted value of the model; $$ y_{j}^{true} $$ is the true value.

After weight optimization, the optimal weights for the two models were determined to be 0.64 for GBR and 0.36 for KRR. The final hybrid model is therefore expressed as:

In this study, the performance of various base machine learning models in predicting the catalytic reaction properties was evaluated. R² was used as the evaluation metric to measure the performance of each model and to make comparisons. Performance was also evaluated by mean absolute error (MAE) and root mean square error (RMSE), as determined using^[33]:

where $$ y_{j}^{pred} $$ is the predicted value of the model; $$ y_{j}^{true} $$ is the true value; $$ \bar{y}^{true} $$ is the mean true value.

Importance analysis and SHAP analysis

To evaluate how each experimental parameter influenced the hybrid model’s predictions, permutation feature importance was applied. We chose PFI because it is model-agnostic and does not depend on the internal workings of a specific algorithm, which makes it particularly suitable for the GBR-KRR hybrid model^[34,35]. In addition, PFI measures the change in model performance when a given feature is perturbed, providing a straightforward way to assess how sensitive the model is to each input variable. In this analysis, the trained model was first used to predict the external test set, and the original coefficient of determination, $$ R_{original}^{2} $$, was recorded. Each input variable was then randomly permuted in turn while all other variables were kept unchanged. The model was used to make predictions on the permuted data, and the corresponding coefficient of determination, $$ R_{permuted}^{2} $$, was calculated. The importance of each feature was expressed as the decrease in R²:

A larger $$ R_{drop}^{2} $$ indicates that permuting the corresponding feature causes a greater loss of model performance, suggesting that the model is more sensitive to that variable^[34-36]. In this study, $$ R_{drop}^{2} $$ was calculated separately for CO₂ conversion, CO yield, and H₂ yield to compare the relative effects of 5 input parameters on each output. It is important to emphasize that PFI reflects the dependence of the trained model on each input variable, rather than establishing a direct causal relationship^[37]. The results were therefore used to identify key operating parameters and to guide subsequent response-trend analysis and condition optimization.

SHAP analysis was further performed to gain a deeper understanding of feature contributions. Unlike PFI, which evaluates the overall importance of a variable, SHAP provides a sample-level decomposition of the prediction into contributions from individual features^[38,39]. For a given output, a positive SHAP value indicates that the feature increases the predicted value relative to the baseline prediction, whereas a negative SHAP value indicates that it decreases the prediction. A larger absolute SHAP value corresponds to a stronger contribution to that specific prediction^[38,39]. For the hybrid model developed in this study, SHAP analysis was used to interpret the prediction behavior of the weighted GBR-KRR model across the experimental domain. By comparing the SHAP distributions of different features for CO₂ conversion, CO yield, and H₂ yield, the analysis helped determine whether key variables had different effects on CO₂ reduction and H₂ formation. This provided additional insights into the nonlinear responses and multi-objective competition in the P²CR system. For interpretability, PFI and SHAP were performed on the five original variables, while the nine engineered descriptors were used only internally in model construction. It is important to emphasize that permutation feature importance and SHAP quantify predictive associations within the experimental domain. These analyses were used to rank the input variables and interpret the behavior of the trained model. Mechanistic explanations based on these results are presented as plausible hypotheses guided by reactor physics and previous literature.

The details of the robustness-oriented strategy

To further assess the extrapolation risk of the generated candidate space, a convex-hull-based applicability-domain analysis was performed using the SPXY training set in the five-dimensional input space. For the feasible candidates satisfying the H₂/CO ratio constraints, the fractions of hull-included points were 50.49%, 49.78%, and 48.66% for H₂/CO = 1 under tolerance windows of ±0.05, ±0.10, and ±0.20, respectively, and 49.52%, 47.85%, and 48.59% for H₂/CO = 2. Importantly, the two final robust recommendations emphasized in this work, corresponding to H₂/CO = 1 (±0.05) and H₂/CO = 2 (±0.05), were both located within the convex hull of the training set. In contrast, some conversion-oriented recommendations under broader tolerance windows were outside the hull, indicating a higher likelihood of extrapolation. After generating the 100,000 candidate conditions, a two-step constrained optimization procedure was applied. First, a hard feasibility filter was used to retain only candidate points whose predicted H₂/CO ratio satisfied the selected tolerance window around the target ratio. Second, within this feasible candidate set, the remaining candidates were ranked using a robustness-oriented score:

where $$ Y_{CO_2} $$ is the predicted CO₂ conversion, $$ \sigma _{CO_2} $$ is the disagreement between the GBR and KRR member models for CO₂ conversion, $$ \sigma _{{H_2}/CO} $$ is the disagreement in the predicted H₂/CO ratio, and D_train is the nearest standardized distance from the candidate point to the training set. The penalty coefficients were selected empirically to preserve CO₂ conversion as the primary optimization objective while discouraging candidates with larger prediction disagreement and greater extrapolation risk.

Model training, evaluation and comparison

The Cu-Pd/TiO₂ photocatalyst was selected based on preliminary catalyst screening and literature-guided catalyst design. Before constructing the machine-learning dataset, several support materials, including TiO₂, Al₂O₃, CeO₂, and ZSM-5, were evaluated. As shown in Supplementary Table 1, among different supports, TiO₂ showed the best overall performance, possibly due to its suitable photoresponse characteristics and compatibility with the plasma reaction environment, which is in good agreement with the results of previous studies^[40]. Therefore, TiO₂ was selected as the model support for subsequent catalyst design. The selection of Cu and Pd was based on their complementary catalytic roles. Cu-containing sites have been widely reported to facilitate CO₂ activation and CO formation, whereas Pd can influence interfacial electron redistribution and hydrogen-involved elementary reaction steps^[41-43]. In our preliminary comparison results [Supplementary Table 1], Cu/TiO₂ exhibited stronger plasma-photocatalytic coupling and higher CO yield, while Pd/TiO₂ promoted H-related product formation. Therefore, Cu and Pd were co-loaded on TiO₂ to combine the CO-forming ability of Cu with the H-related reaction regulation of Pd and Cu-Pd/TiO₂ was used as a representative model catalyst to establish and validate the machine-learning-guided optimization framework. To assess the synergistic effect in the P²CR system, control experiments were conducted to illustrate the synergistic effect of this system, as shown in Supplementary Figure 2. The light-only experiment produced only trace amounts of CO (0.013 mmol g^-1 h^-1) and negligible CO₂ conversion, indicating that under the current conditions, the contribution of photocatalysis to CO₂ reduction is negligible. In contrast, the CO yield using plasma alone was 13.93 mmol g^-1 h^-1 with 1.4% CO₂ conversion, while the plasma-photocatalysis combined conditions significantly increased the CO yield to 28.52 mmol g^-1 h^-1 (2.86% CO₂ conversion), far exceeding the yield achieved by plasma alone. These results clearly demonstrate that light irradiation can effectively promote the plasma-assisted CO₂ reduction process, thereby significantly increasing CO production, demonstrating the coupling and synergistic effect of this P²CR system. Supplementary Figures 3-8 illustrate the detailed characterizations of Cu-Pd/TiO₂ photocatalyst. The results of Gas Chromatography (GC) chromatograms in Supplementary Figure 9 show that CO was identified as the only detectable carbon-containing product without any other carbon-containing products in this system. Consistent with this observation, the carbon balance remained between 99.70% and 99.93% across 20 independent experimental runs [Supplementary Table 2], indicating good carbon closure and supporting the reliability of the product quantification. In addition, the surface temperatures of the reactor during reaction were measured by infrared thermal images to investigate the thermal effect generated by light and plasma. As shown in Supplementary Figure 10, both light and plasma caused an increase in temperature. To eliminate the influence caused by thermal effects, a heat-only control experiment under comparable external temperature conditions (temperature from 30 to 100 °C) was conducted. However, no CO, H₂ or other products were detected, indicating that thermal heating alone was insufficient to drive the observed CO₂ conversion and syngas formation in this system. Moreover, Cu-Pd/TiO₂ was further compared with other state-of-the-art photocatalysts for syngas production [Supplementary Table 3]. Most reported systems exhibited relatively modest gas productivity, with CO and H₂ yields generally reported at the μmol g^-1 h^-1 level. In addition, their H₂/CO ratios are typically distributed within a comparatively narrow range of 0.31:1-6.00:1, limiting the flexibility of syngas composition control. By comparison, the present Cu-Pd/TiO₂ achieved maximum observed CO and H₂ yields of 56.42 and 53.71 mmol g^-1 h^-1, respectively, and enabled a wide range of H₂/CO ratios (0.022:1-53.71:1). These results indicate that the Cu-Pd/TiO₂ photocatalyst in the present system provides both high syngas productivity and substantially broader flexibility in H₂/CO-ratio regulation.

Based on 120 experimental runs in Supplementary Tables 4 and 5, the hybrid model was trained and tested. As shown in Figure 2A, the proposed hybrid model achieved the highest R², with a value of approximately 0.996. It slightly outperformed KRR and GBR, which achieved R² values of approximately 0.992 and 0.987, respectively. Compared with traditional models like K-Nearest Neighbors (KNN) (0.84) and Decision Tree regressors (0.89), the hybrid model showed larger absolute R² improvements of approximately 0.16 and 0.11, respectively. These results indicate that the hybrid architecture more effectively captures the nonlinear relationships embedded in the experimental dataset. Figure 2B-D further compare the predictive performance of different models for CO₂ conversion, CO yield, and H₂ yield on both training and test sets. For CO₂ conversion [Figure 2B], the hybrid model achieves a test-set R² of 0.947, compared with 0.921 for KRR and 0.940 for GBR, corresponding to increases of 0.026 and 0.007, respectively. It also achieves the lowest test-set RMSE (0.271) and a tied-lowest test-set MAE (0.221, equal to GBR). For CO yield [Figure 2C], the hybrid model reaches an R² of 0.950 on the test set, slightly outperforming KRR (0.945) and GBR (0.934), demonstrating improved stability across both training and testing domains. For H₂ yield [Figure 2D], the hybrid model achieves a test-set R² of 0.954, higher than KRR (0.928) and slightly higher than GBR (0.950). The hybrid model has a lower test-set MAE than GBR; however, its test-set RMSE (1.60) is slightly higher than that of GBR (1.50). These results indicate a balanced error profile rather than consistently lower errors across all evaluation metrics. Parity plots in Figure 3A-C further support these results, with the training and test data distributed around the fitted lines. Together, these analyses indicate that the hybrid model achieves a balance between training accuracy and test-set generalization, providing accurate and robust predictions for all three outputs. The model is therefore well suited to multi-objective prediction of the three reaction targets. To further assess the predictive performance of the hybrid model, 10 unseen experimental conditions were generated within the original experimental ranges and evaluated using the hybrid model. As shown in Supplementary Tables 6 and 7, the predicted values were in close agreement with the corresponding experimental results, further supporting the predictive capability of the hybrid model for this P²CR system. The correlation matrix of all variables is shown in Supplementary Figure 11. To assess whether the predictive performance of the models depended on catalyst-mass normalization, additional models were developed to predict the absolute CO and H₂ production rates in Supplementary Table 8.

Figure 2. Performance comparison of the machine-learning models. (A) Overall comparison based on the training-set R²; Performance of the hybrid model, KRR and GBR for (B) CO₂ conversion, (C) CO yield and (D) H₂ yield. RMSE: Root mean square error; MAE: mean absolute error; MSE: mean squared error; SPXY: sample set partitioning based on joint X-Y distances; GBR: gradient boosting regressor; KRR: kernel ridge regression; RF: random forest; SVR: support vector regression; BPANN: backpropagation artificial neural network; KNN: K-nearest neighbors.

Figure 3. Predicted versus experimental values for (A) CO₂ conversion, (B) CO yield and (C) H₂ yield; Permutation importance of five input parameters for (D) CO₂ conversion, (E) CO yield and (F) H₂ yield.

Importance analysis of different parameters

To further assess the sensitivity of the model predictions to the operating variables, an R²-drop permutation analysis was performed to quantify their relative importance, as shown in Figure 3D-F. Relative humidity was identified as the most influential variable across three outputs, followed by light intensity and discharge power, whereas gas flow and catalyst dosage showed comparatively smaller contributions. These rankings describe the sensitivity of the trained model within the investigated domain and should not be interpreted as direct evidence of mechanistic importance. The importance of relative humidity may reflect the influence of water participation and the reaction environment on the predicted outputs. These effects could be associated with changes in surface reaction conditions and interfacial electron or proton transfer processes^[44,45]. The importance of light intensity may reflect its association with photocatalyst excitation and the resulting changes in the model prediction^[46]. Similarly, the importance of discharge power may reflect the influence of plasma energy input on the discharge environment and the associated reaction conditions^[20,47]. Gas flow rate and catalyst dosage showed lower overall importance than relative humidity, light intensity, and discharge power. For gas flow rate, its influence was more pronounced for CO₂ conversion and CO yield than for H₂ yield. Figure 3D-F presents permutation-based model importance rather than direct causal response curves. Thus, the analysis identifies the variables to which the model predictions are most sensitive and provides guidance for operating-condition optimization.

Because the operating variables are strongly coupled, their combined effects on the reaction outputs must be considered when interpreting the P²CR system. We therefore used the hybrid machine-learning model to examine the response trends associated with the most influential variables. Based on the R²-drop analysis, discharge power, relative humidity and light intensity were selected for detailed response-trend analysis. As shown in Figure 4A and B, the model predictions closely followed the experimental trends, consistent with the high R² values and low MAE and RMSE values. These results indicate that the hybrid model captured the nonlinear response behavior of the P²CR system. Under the conditions examined, CO₂ conversion and CO yield reached their maximum values at a discharge power of 40 W and decreased at higher power. One possible explanation is the non-uniform electric-field distribution within the square reactor. The reactor geometry may produce local electric-field enhancement or weakening near the corners and edges, thereby affecting the spatial distribution of the discharge and reactive species^[48-51]. However, this explanation should be regarded as a hypothesis. Another possible explanation is that excessive discharge power may also induce local heating or alter the distribution of reactive species, thereby affecting the apparent catalytic performance^[47]. In contrast, H₂ formation increased with increasing power. This trend may reflect the different responses of CO₂ reduction and hydrogen formation to increasing energy input. The greater thermodynamic stability of CO₂ and the potentially more accessible pathway for hydrogen formation possibly favor H₂ production under higher-power conditions^[45,52]. These results suggest that moderate discharge power is a critical operating window in this system, reflecting the nonlinear role of power in regulating reactive species generation and reaction kinetics in the P²CR process.

Figure 4. Comparison of model prediction with experimental data for the effect of discharge power on the plasma-photocatalytic CO₂ and H₂O conversion: (A) CO₂ conversion and (B) CO yield and H₂ yield (Relative humidity = 58%, light intensity = 1,000 mW cm^-2, gas flow = 30 mL min^-1, catalyst dosage = 40 mg); Predicted effects of (C) relative humidity (Discharge power = 50 W, light intensity = 1,000 mW cm^-2, gas flow = 20 mL min^-1, catalyst dosage = 60 mg) and (D) light intensity (Discharge power = 50 W, relative humidity = 32%, gas flow = 20 mL min^-1, catalyst dosage = 60 mg) on the plasma-photocatalytic CO₂ and H₂O conversion reaction performance.

Figure 4C further illustrates the effect of relative humidity on reaction outputs, while Supplementary Figure 12 compares the experimental and predicted values. Increasing the relative humidity from 32% to 58% decreased CO₂ conversion from 5.31% to 2.27% and CO yield from 50.67 to 12.19 mmol g^-1 h^-1. In contrast, H₂ yield increased from 2.91 mmol g^-1 h^-1 to 16.32 mmol g^-1 h^-1, which is consistent with the literature^[45,53-55]. The increased water content may suppress the plasma discharge and thereby reduce the effective discharge density or modify electron-energy distribution^[53]. A further possible explanation is that water-derived hydroxyl radicals could participate in secondary reactions involving CO intermediates and potentially promote CO reoxidation to CO₂^[53,55]. This interpretation is proposed as a mechanistic hypothesis based on previously reported reaction pathways. Increased proton availability may also contribute to enhanced hydrogen formation, consistent with observations in other non-thermal plasma systems^[20,54]. Overall, the model-predicted trends identify relative humidity as an important operating variable for regulating the balance between CO₂ reduction and H₂ formation, although the underlying elementary pathways remain to be established experimentally.

Figure 4D and Supplementary Figure 13 show the model-predicted influence of light intensity on the reaction outputs. A similarly nonlinear response was observed. Under the selected conditions, CO₂ conversion and CO yield reached their maximum values at an intermediate light intensity of approximately 1,000 mW cm^-2, with values of 5.31% and 50.67 mmol g^-1 h^-1, respectively. This indicates that moderate illumination may enhance photocatalyst excitation and facilitate the participation of photogenerated charge carriers in CO₂ reduction in this P²CR system, potentially in conjunction with plasma-induced activation^[20,56]. However, further increasing the light intensity decreased both CO₂ conversion and CO yield, whereas H₂ yield increased from 1.33 to 4.07 mmol g^-1 h^-1. This trend suggests that excessive illumination may favor water-related reduction and H₂ formation in this system^[46]. Overall, these results indicate that light intensity has an optimal window in the P²CR system with both insufficient and excessive illumination being unfavorable for maximizing CO₂ reduction. Supplementary Figure 14 shows the local model-predicted response to gas flow rate while discharge power, light intensity, relative humidity, and catalyst dosage were held constant. Increasing the gas flow rate from 20 to 60 mL min^-1 caused an overall decrease in CO₂ conversion and CO yield. H₂ yield also decreased, but the decline was less pronounced than the declines observed for CO₂ conversion and CO yield. Gas flow rate affects the reaction through both residence-time and throughput effects. In the present reactor, the effective discharge volume was approximately 20 cm³. Increasing the total gas flow rate from 20 to 60 mL min^-1 therefore reduced the nominal gas residence time from approximately 60 to 20 s. The shorter residence time may reduce the interaction time among CO₂, plasma-generated energetic species, and subsequent surface reduction reactions. This effect could account for the decrease in CO₂ conversion. CO yield showed a similar response because CO formation is closely linked to the extent of CO₂ reduction and may require sufficient interaction time for the formation and desorption of CO intermediates. The weaker response of H₂ yield suggests that the H₂-forming pathway is less sensitive to gas flow rate than the CO-producing pathway. This is likely because H₂ formation does not require the same sequence of CO₂ activation and CO-intermediate formation as the CO-producing pathway. Consequently, H₂ yield is affected by gas flow rate to a lesser extent. The model-predicted response to catalyst dosage and the corresponding model-experiment correlations for catalyst dosage are provided in Supplementary Figure 15. This target-dependent behavior means that maximizing CO₂ conversion alone is insufficient to guarantee the desired syngas ratio. It is therefore necessary to combine model interpretation with constrained optimization for experimental condition screening.

SHAP analysis

To further examine how the operating parameters contributed to the model predictions, SHAP analysis was performed across the experimental domain^[38,39]. As shown in Figure 5A-C, relative humidity, light intensity, and discharge power were identified as the most influential predictors for CO₂ conversion, CO yield and H₂ yield, consistent with the R²-drop analysis. SHAP analysis also revealed the direction and distribution of each feature’s contribution across individual samples. For CO₂ conversion and CO yield, samples with high relative humidity were mainly located in the negative SHAP region, whereas samples with lower humidity were more associated with positive SHAP values. Thus, higher humidity was associated with lower predicted CO₂ conversion and CO yield. By contrast, high humidity was generally associated with positive SHAP values for H₂ yield. This output-dependent pattern is consistent with the response-trend analysis.

Figure 5. SHAP-value distribution for the five input parameters for (A) CO₂ conversion, (B) CO yield and (C) H₂ yield; (D) Optimization results of the hybrid model under H₂/CO-constraints. SHAP: SHapley Additive exPlanations.

The SHAP distributions for light intensity and discharge power showed a pronounced nonlinear pattern. For CO₂ conversion and CO yield, moderate light intensity and discharge power were generally associated with positive SHAP contributions, whereas higher values did not further increase, and in some cases decreased, the model predictions. This indicates that the hybrid model captured an optimal operating window within the investigated domain. For H₂ yield, higher relative humidity, light intensity, and discharge power were generally associated with positive SHAP contributions, indicating that the model predictions were sensitive to these variables within the investigated range. By comparison, gas flow rate and catalyst dosage showed relatively small contributions to the model predictions between 30 and 60 mg catalyst dosage and across the investigated flow-rate range. Gas flow rate nevertheless showed a more noticeable contribution to the predictions of CO₂ conversion and CO yield than to H₂ yield. Overall, SHAP analysis provides an interpretable description of the positive and negative contributions of the input variables to the model predictions. These findings indicate that the model captured nonlinear input-output relationships within the P²CR system while maintaining good predictive performance across the investigated experimental conditions. Because global feature-importance measures do not fully describe conditional effects between operating variables, a low-high 2 × 2 conditional interaction analysis was additionally performed. The analysis procedure and complete results are provided in Supplementary Table 9.

Hybrid model application

The importance, response-trend, and SHAP analyses collectively indicate that the P²CR system exhibits strongly nonlinear, output-dependent behaviors. Relative humidity, light intensity, and discharge power produced different responses for CO₂ conversion, CO yield, and H₂ yield. In particular, conditions that favored CO₂ conversion and CO formation did not necessarily produce the desired H₂/CO ratio. Therefore, the trained hybrid model was applied to constrained optimization, aiming to identify operating conditions that satisfied prescribed H₂/CO ratios while maintaining relatively high CO₂ conversion. A total of 100,000 candidate conditions were generated by random sampling within the experimental ranges of the five operating variables. The hybrid model was used to predict CO₂ conversion, CO yield, and H₂ yield for each candidate, from which the corresponding H₂/CO ratio was calculated. H₂/CO ratios of 1 and 2 were selected as representative targets for downstream syngas applications. An H₂/CO ratio of 1 is relevant to oxo-synthesis, whereas a ratio of 2 is commonly associated with methanol synthesis and Fischer-Tropsch synthesis^[57,58]. Among the 100,000 generated candidate conditions, 47,245 (47.2%) were located within the five-dimensional convex hull of the SPXY training set, whereas 52,755 (52.8%) fell outside the hull [Supplementary Figure 16]. Nevertheless, the large fraction of candidate conditions outside the hull highlights the potential risk of extrapolation when screening the broader hypothetical design space. Candidate conditions satisfying tolerance windows of ±0.05, ±0.10 and ±0.20 were screened. Among the feasible candidates, the condition with the highest predicted CO₂ conversion was selected as the conversion-oriented recommendation. Because predictions outside the training domain may be less reliable, the highest-conversion candidate was not necessarily considered the most robust choice^[59,60]. We therefore introduced a robustness-oriented recommendation strategy that considered predicted CO₂ conversion, disagreement between the GBR and KRR models, deviation from the target H₂/CO ratio and distance from the training-data distribution. Smaller model disagreement, lower ratio error and greater proximity to the experimental data were considered indicators of lower prediction risk^[60-62]. As shown in Figure 5D, each point represents a candidate reaction condition. A trade-off was observed between CO₂ conversion and syngas composition. Candidates with higher predicted CO₂ conversion were generally concentrated in the lower-H₂/CO region, whereas CO₂ conversion tended to decrease as the H₂/CO ratio increased. This indicates that high CO₂ conversion and a prescribed syngas composition cannot be optimized simultaneously without imposing an explicit ratio constraint^[45,54]. The two final recommended conditions with a tolerance of ±0.05 were therefore selected under the specified H₂/CO constraint (1:1 and 2:1). Importantly, these two conditions were located within the training-set convex hull. The experimental validation results in Supplementary Tables 10 and 11 were consistent with the model predictions, supporting the use of the hybrid model for operating-condition screening within the investigated P²CR domain. In addition, CO productivity per unit plasma power was calculated for the two recommended conditions and is presented in Supplementary Table 12. The condition targeting an H₂/CO ratio of 1 achieved a CO productivity normalized by plasma power of 16.5 ± 0.9 mmol kWh^-1, whereas the condition targeting an H₂/CO ratio of 2 achieved 9.8 ± 0.3 mmol kWh^-1. These results indicate that the H₂/CO = 1 condition was more favorable for CO production per unit plasma power, whereas the H₂/CO = 2 condition produced a more H₂-rich syngas composition.