Predicting Methane Dry Reforming Performance via Multi-Output Machine Learning: A Comparative Study of Regression Models

Abstract

Dry reforming of methane (DRM) offers a sustainable route to convert two major greenhouse gases—CH₄ and CO₂—into synthesis gas (syngas), enabling low-carbon hydrogen production and carbon utilization. This study applies fifteen machine learning (ML) regression models to simultaneously predict CH₄ conversion, CO₂ conversion, H₂ yield, and CO yield using a published dataset of 27 experiments with Ni/CaFe₂O₄-catalyzed DRM. The comparative evaluation covers linear, tree-based, ensemble, and kernel-based algorithms under a unified multi-output learning framework. Feature importance analysis highlights reaction temperature, CH₄/CO₂ feed ratio, and Ni metal loading as the most influential variables. Predictions from the top-performing models (CatBoost and Random Forest) identify optimal performance windows—feed ratio near 1.0 and temperature between 780–820 °C—consistent with thermodynamic and kinetic expectations. Although no new catalysts are introduced, the study demonstrates how ML can extract actionable parametric insights from small experimental datasets, guiding future DRM experimentation and process optimization for hydrogen-rich syngas production.

1. Introduction

Dry reforming of methane (DRM) is an attractive process for simultaneously converting two major greenhouse gases, CH₄ and CO₂, into synthesis gas (syngas), a versatile feedstock for hydrogen production and downstream chemical synthesis. While extensive experimental work has advanced catalyst development for DRM, data-driven approaches can complement these efforts by predicting process performance and identifying promising operating conditions without exhaustive laboratory trials. In this study, we evaluate fifteen machine learning (ML) regression models using a published dataset of 27 experiments on Ni/CaFe₂O₄-catalyzed DRM. The models predict CH₄ conversion, CO₂ conversion, H₂ yield, and CO yield simultaneously, providing a comparative assessment of algorithm performance and revealing parameter interactions. Although this work does not introduce new catalyst formulations, it offers predictive insights that can inform future experimental optimization of DRM for sustainable syngas generation and low-carbon hydrogen production.

Sustainable energy source is essential for mitigating climate change and reducing greenhouse gas emissions. Hydrogen is a key clean energy carrier with potential applications across transportation, power generation, and industry. Among H₂ production pathways, dry reforming of methane (DRM) has attracted attention for its dual benefit: converting CH₄ and CO₂, two major greenhouse gases into H₂-rich syngas [1,2,3,4,5].

Steam methane reforming (SMR), the dominant hydrogen production route, is energy-intensive and emits large volumes of CO₂. In contrast, dry reforming of methane (CH₄ + CO₂ → 2CO + 2H₂) offers a more sustainable alternative by consuming CO₂ as a reactant and producing syngas. However, the endothermic nature of DRM requires high temperatures (700–900 °C), which can lead to catalyst deactivation via carbon deposition and sintering, limiting its commercial viability [6,7,8,9,10,11,12,13,14,15,16,17,18].

Table 1. Comparison of Hydrogen Production Methods.

Hydrogen Production Method	Reaction	Feedstocks	Typical H2/CO Ratio	CO2 Emissions (kg CO2/kg H2)	Energy Efficiency	Fuel Relevance
Steam Methane Reforming (SMR) [19,20]	CH4 + H2O → CO + 3H2	CH4, H2O (steam)	~3.0	~9–11	~65–75%	Dominant method; high emissions
Dry Reforming of Methane (DRM) [8,9]	CH4 + CO2 → 2CO + 2H2	CH4, CO2	~1.0	~5–7	~55–65%	Syngas for Fischer–Tropsch, methanol, SNG
Electrolysis (Renewable) [21]	H2O → H2 + ½O2 (via electricity)	Water + Renewable Power	∞ (pure H2)	0 (if fully renewable)	~60–70%	Green hydrogen; no carbon-based fuel generated

compares key hydrogen production pathways, emphasizing the strategic relevance of DRM for low-carbon syngas generation. The balanced H₂/CO ratio and moderate emissions make DRM particularly suitable for downstream fuel synthesis, aligning with sustainable energy technologies focus.

1.1. Contributions to SDG 7 (Affordable and Clean Energy)

This research aligns with Sustainable Development Goals (SDG) 7 and 13 by advancing cleaner hydrogen production through methane dry reforming. By applying machine learning to improve DRM efficiency, the study supports carbon utilization strategies that reduce greenhouse gas emissions and convert waste gases into valuable energy carriers.

1.2. Scope and Research Objectives

This study aims to improve the predictive accuracy and interpretability of DRM performance using machine learning. Experimental data from Ni/CaFe₂O₄-catalyzed DRM are used to model four key outputs: CH₄ conversion, CO₂ conversion, H₂ yield, and CO yield. Since traditional models often fail to capture nonlinear process interactions, we evaluate a range of regression algorithms—including ensemble, support vector, and Bayesian models—for multi-output prediction. We also assess how feature engineering, polynomial expansions, interaction terms, and outlier treatment influence model performance. The findings support both scientific insight and operational optimization of DRM for low-carbon hydrogen generation.

2. Materials and Methods

This study utilizes experimental data from published DRM experiments employing a Ni/CaFe₂O₄ catalyst [7]. The dataset includes 27 observations, each representing a unique combination of process parameters: feed ratio, temperature, and metal loading. Target outputs are CH₄ conversion, CO₂ conversion, H₂ yield, and CO yield—key indicators of DRM efficiency and hydrogen production performance. This study uses only the data from [7]. Software versions: scikit-learn==1.3; CatBoost == 1.2.7;

2.1. Feature Set

The dataset consists of three input variables—feed ratio (CH₄/CO₂), temperature (°C), and Metal Loading (%)—known to influence DRM performance. The outputs include CH₄ and CO₂ conversion; H₂ and CO yield (all in %), which reflect key indicators of reaction efficiency and H₂ productivity.

Table A1. Experimental data for the DRM reactions [7].

Expt. Runs	Inputs			Outputs
	Feed Ratio	Reaction Temp (°C)	Metal Loading (%)	CH4 Conversion (%)	CO2 Conversion (%)	H2 Yield (%)	CO Yield (%)
1	0.40	800.00	10.00	22.99	20.84	13.24	14.56
2	0.70	800.00	15.00	88.63	85.41	70.31	73.21
3	0.40	750.00	15.00	23.43	20.68	13.54	14.37
4	1.00	700.00	5.00	59.08	56.97	26.22	28.32
5	1.00	700.00	15.00	25.38	33.52	16.35	17.70
6	1.00	750.00	10.00	39.60	38.98	21.11	23.32
7	0.40	700.00	5.00	25.01	21.96	13.26	14.31
8	0.40	800.00	15.00	34.48	30.02	20.32	19.44
9	1.00	800.00	10.00	50.70	47.60	26.43	27.31
10	0.40	750.00	5.00	30.34	26.32	16.17	15.31
11	0.70	750.00	15.00	33.45	22.22	19.15	19.15
12	0.70	800.00	10.00	26.11	27.77	14.54	16.59
13	0.40	700.00	10.00	17.69	14.15	11.12	13.09
14	0.70	700.00	10.00	23.27	20.35	13.21	13.83
15	0.40	700.00	15.00	19.78	16.31	13.37	13.37
16	0.70	750.00	5.00	32.89	30.02	17.15	18.32
17	1.00	750.00	5.00	62.93	62.34	32.36	33.31
18	1.00	750.00	15.00	52.76	51.85	30.77	30.77
19	0.70	700.00	15.00	25.82	21.34	12.45	17.70
20	0.70	800.00	5.00	35.09	33.77	33.77	25.54
21	1.00	700.00	10.00	38.75	35.68	18.78	19.11
22	0.70	700.00	5.00	27.46	23.15	14.14	15.32
23	0.70	750.00	10.00	23.78	21.13	13.56	15.06
24	1.00	800.00	15.00	90.04	87.60	73.42	74.43
25	0.40	800.00	5.00	35.10	31.62	20.64	22.41
26	0.40	750.00	10.00	22.16	19.60	12.21	13.39
27	1.00	800.00	5.00	67.93	66.39	35.36	38.31

(Appendix A) summarizes these variables.

2.2. Feature Engineering

Feature engineering was applied to improve model accuracy by generating polynomial and interaction terms from the original inputs. Examples include Feed Ratio × Temperature and Temperature × Metal_loading, designed to capture nonlinear dependencies. These engineered features were assessed for their contribution to model performance and retained based on predictive significance [22,23,24].

Original Features: Feed_ratio, Reaction_Temp, Metal_loading. Polynomial Features: Feed_ratio², Reaction_Temp², Metal_loading², Feed_ratio × Reaction_Temp, Feed_ratio × Metal_loading, Reaction_Temp × Metal_loading.

2.3. Machine Learning Regression Models for DRM

DRM is influenced by competing side reactions such as reverse water-gas shift, methane cracking, and the Boudouard reaction, making traditional models complex and computationally intensive [8]. Machine learning (ML) techniques, particularly multi-output regression models, provide an efficient alternative by accurately predicting multiple DRM outcomes simultaneously. Fifteen regression models were selected to provide a diverse set of approaches capable of capturing complex nonlinear relationships, managing small sample sizes, and improving prediction robustness. These fifteen regression models were evaluated across diverse algorithm families, including:

Linear Regression (LR): A baseline linear approach assuming a direct proportionality between inputs and outputs. Useful for initial comparison but limited in handling nonlinearity.

Ridge Regression: A linear model with L2 regularization to reduce overfitting and manage multicollinearity, suitable for small datasets.

Lasso Regression: Employs L1 regularization enabling feature selection by shrinking coefficients of less relevant features to zero.

Elastic Net: Combines L1 and L2 penalties to balance feature selection and coefficient shrinkage.

Bayesian Ridge Regression: Provides probabilistic estimates and incorporates regularization within a Bayesian framework, beneficial for small datasets with noisy data.

Support Vector Regression (SVR): Employs kernel methods to capture nonlinear relationships by projecting data into higher-dimensional spaces.

Random Forest Regression: An ensemble of decision trees that reduces variance by averaging multiple trees, effective at capturing nonlinearities and interactions without requiring data scaling.

Extra Trees Regression: Similar to Random Forest but with more randomization in splitting, often improving variance reduction.

Gradient Boosting Regression: Builds additive models in a forward stage-wise fashion, optimizing prediction accuracy via gradient descent on residual errors.

AdaBoost Regression: Focuses on reducing errors by weighting difficult-to-predict samples higher in successive iterations.

K-Nearest Neighbours Regression: A non-parametric method predicting outputs based on local neighbourhoods in input space.

Decision Tree Regression: Simple tree-based method capturing nonlinearities via hierarchical partitioning of input space.

Polynomial Regression: Extends linear models by including polynomial features to model nonlinear trends explicitly.

Multi-layer Perceptron (MLP): A feed-forward neural network capable of learning complex nonlinear functions given sufficient data and regularization.

Gaussian Process Regression: A Bayesian non-parametric approach modelling distributions over functions, well-suited for quantifying prediction uncertainty.

These models complement each other by balancing bias-variance trade-offs, interpretability, and computational complexity. Considering the limited dataset size (n = 27), regularized and ensemble methods were emphasized to prevent overfitting while capturing essential nonlinear behaviours of DRM reactions [25,26,27,28,29,30,31,32]. A flowchart summarizing model training and evaluation is illustrated in Figure 1.

2.4. Model Training and Validation

Models were trained using a 90:10 split and optimized via GridSearchCV with 3-fold and 5-fold cross-validation. LOOCV was also applied to enhance generalizability given the small dataset (n = 27). All models were implemented in Python (scikit-learn == 1.3) and evaluated using MAE, RMSE, and R². Optimized models were applied to predict CH₄ Conversion, CO₂ Conversion, H₂ Yield, and CO Yield. Predictions were validated against experimental data, and top-performing models were identified for potential real-world DRM deployment [26,27,33,34,35,36,37].

2.5. Performance Metrics

The conversion rates of CH₄ and CO₂ and the yields of H₂ and CO were calculated as shown in Appendix B.

Model performance was evaluated using the following metrics [34,38]: Mean Absolute Error (MAE)—average magnitude of prediction error; Root Mean Square Error (RMSE)—penalizes larger deviations, reflecting error stability; R² Score—indicates variance explained by the model; Mean Absolute Percentage Error (MAPE)—enables scale-independent error comparison.

2.6. Preprocessing the Data

To ensure comparability across features, the dataset was standardized using z-score normalization, computed as (Equation (1)):

$$\mathrm{Z}={\displaystyle \frac{\mathrm{X}-\mathsf{\mu }}{\mathsf{\sigma }}}$$

(1)

where X is the original data point, μ is the mean of the feature σ is the standard deviation of the feature. This transformation scales all features to a mean of 0 and a standard deviation of 1, facilitating effective model training.

2.7. Descriptive Statistics Summarizing the Main Characteristics of the Data

Table 2. Descriptive statistics of the data.

	Feed Ratio	Reaction Temp	Metal Loading	CH4 Conversion	CO2 Conversion	H2 Yield	CO Yield
count	27.00	27.00	27.00	27.00	27.00	27.00	27.00
mean	0.70	750.00	10.00	38.32	35.84	23.07	23.98
std	0.25	41.60	4.16	19.93	20.24	15.77	15.84
min	0.40	700.00	5.00	17.69	14.15	11.12	13.09
25%	0.40	700.00	5.00	24.39	21.24	13.46	14.81
50%	0.70	750.00	10.00	32.89	30.02	17.15	18.32
75%	1.00	800.00	15.00	45.15	43.29	26.33	26.43
max	1.00	800.00	15.00	90.04	87.60	73.42	74.43

summarizes key variables—Feed Ratio, Reaction Temperature, Metal Loading, CH₄ Conversion, CO₂ Conversion, H₂ Yield, and CO Yield—based on 27 experimental observations. The mean values are Feed Ratio: 0.70, Reaction Temperature: 750 °C, Metal Loading: 10%, with CH₄ and CO₂ conversions averaging 38.32% and 35.84%, respectively.

2.8. Outlier Detection

Potential outliers were identified using the Interquartile Range (IQR) method, calculated as (Equation (2)):

IQR = Q3 − Q1

(2)

Outliers fall outside the range: Upper Bound= Q3 + 1.5 × IQR; Lower Bound = Q1 − 1.5 × IQR.

Table 3. Identifying potential outliers.

Variable	Q1	Q3	IQR	Lower Bound	Upper Bound	Potential Outliers
Feed_ratio	0.40	1.00	0.60	−0.50	1.90	None
Reaction_Temp	700.00	800.00	100.00	550.00	950.00	None
Metal_loading	5.00	15.00	10.00	−10.00	30.00	None
CH4_conversion	24.39	45.15	20.76	−6.75	76.29	<−6.75; >76.29
CO2_conversion	21.24	43.29	22.05	−11.83	76.36	<−11.83; >76.36
H2_yield	13.46	26.33	12.87	−6.85	46.64	<−6.85; >46.64
CO_yield	14.81	26.43	11.62	−2.62	43.86	<−2.62; >43.86

highlights variables where extreme values were detected. CH₄ and CO₂ conversions exhibited greater variability, suggesting sensitivity to reaction conditions. Outliers were analyzed for their impact on model performance and handled accordingly.

2.9. Visualizing the Data

Pair plots (Figure 2) provide an overview of feature relationships and correlations. The sns.pairplot function was used to create scatter plots for all numerical variables, with colours representing reaction temperature (hue = ‘Reaction_Temp’) to highlight temperature-dependent trends. Diagonal Histograms Show variable distributions, revealing skewed trends in CH₄ and CO₂ conversions, indicating a higher frequency of lower conversion values.

Bivariate Relationships: CH₄ and CO₂ conversions exhibit a strong positive correlation, indicating that they are influenced by similar reaction conditions. Likewise, H₂ and CO yields are positively correlated, suggesting that these products are generated through concurrent pathways. Analysis of feed ratio versus conversion reveals that higher reaction temperatures—represented by green and yellow data points—are associated with increased CH₄ and CO₂ conversion rates, particularly at elevated feed ratios. Additionally, both increased metal loading and higher temperatures contribute to improved conversion efficiency. The presence of distinct clusters in feed ratio and metal loading data further suggests categorical influences, likely reflecting specific experimental setups or catalyst formulations.

Colour Distribution and Temperature Trends: The distribution of data points by colour reveals clear temperature-dependent trends in DRM performance. Purple and blue points, which correspond to lower reaction temperatures (~700 °C), tend to cluster around lower CH₄ and CO₂ conversion values. In contrast, green and yellow point indicative of higher temperatures (~800 °C) are associated with significantly higher conversion rates and syngas (H₂ and CO) yields. These visual patterns underscore the critical role of temperature in enhancing reaction efficiency. Moreover, such insights are valuable for feature selection and model training, reinforcing key trends that can improve the predictive accuracy of machine learning models.

3. Results and Discussion

This section presents a comprehensive evaluation of model performance, including correlation analysis, hyperparameter optimization via GridSearchCV, cross-validation outcomes, and regression metrics. Results are contextualized for practical applications in catalytic processes, particularly DRM.

3.1. Model Evaluation

The machine learning models were evaluated to identify the most effective algorithms for predicting DRM outputs. Model performance was assessed using the metrics outlined in Section 2.5, with a focus on accuracy and generalizability across all four targets.

A range of 15 regression models was assessed to predict CH₄ conversion, CO₂ conversion, H₂ yield, and CO yield. Models included linear (Ridge, Lasso), regularized (ElasticNet), ensemble (Random Forest, Gradient Boosting, XGBoost, CatBoost, LightGBM), and kernel-based methods (SVR, NuSVR, Kernel Ridge), along with neural networks (MLP Regressor) and Bayesian Ridge. Model selection considered the ability to handle non-linear relationships, multicollinearity, and interaction effects, particularly for key variables like Feed Ratio and Reaction Temperature:

• Ensemble methods and neural networks captured complex patterns via multiple learners or layers.
• Kernel methods (SVR, NuSVR) effectively modelled non-linearities via feature space transformations.
• Regularized models (Ridge, Lasso, ElasticNet) addressed multicollinearity by penalizing large coefficients.
• Bayesian Ridge introduced probabilistic regularization via priors.

Models like Random Forest, Gradient Boosting, and CatBoost also offer feature importance metrics. While feature ranking is outside this paper’s scope, it provides potential for future insights [28,29,30,31,32]. The following sections summarize the impacts of feature engineering, model comparisons, and multi-output prediction performance.

3.2. Correlation Analysis

The correlation matrix presented in Figure 3 was generated using Pearson Correlation Coefficients (PCCs) to assess linear relationships among features and outputs. While some correlations—such as the positive association between reaction temperature and CH₄ conversion—reflect well-known thermodynamic principles, the purpose of this analysis is primarily methodological. Specifically, it serves to:

(1) check data consistency and identify any anomalous trends prior to model development, and

(2) inform feature engineering by identifying variables and interactions with strong predictive influence.

Table 4. Pearson Correlation Coefficients (PCC) between input features and DRM outputs.

Feature	CH4 Conversion	CO2 Conversion	H2 Yield	CO Yield
Feed Ratio	0.59	0.64	0.43	0.44
Reaction Temperature	0.43	0.50	0.46	0.42
Metal Loading	0.31	0.29	0.33	0.37
Feed Ratio × Temperature	0.66	0.70	0.58	0.61

summarizes these correlations. Feed Ratio and Reaction Temperature exhibit the strongest positive correlations with CH₄ and CO₂ conversions (PCC = 0.59–0.70), confirming their dominant influence on DRM performance. Interaction terms, particularly Feed Ratio × Reaction Temperature, show even higher correlations (up to 0.70), justifying their inclusion as engineered features in the modeling pipeline. Although these findings align with established DRM trends, their primary role here is to enhance ML model interpretability and reduce the risk of introducing spurious relationships during feature generation.

3.3. Prediction Models and Hyperparameter Tuning

Fifteen regression models were evaluated using GridSearchCV with 3-fold and 5-fold cross-validation. Key hyperparameters were optimized for each model, balancing complexity and accuracy.

3.3.1. GridSearchCV Results

GridSearchCV provided robust hyperparameter tuning (

Table A2. Model metrics for original features using Grid Search CV (for CV = 3 and CV = 5).

Model	Metric	CV = 3, Original	CV = 5, Original
Linear	CH4_conversion	Train R2 = 0.55, Test R2 = 0.24	Train R2 = 0.55, Test R2 = 0.24
	CO2_conversion	Train R2 = 0.60, Test R2 = 0.09	Train R2 = 0.60, Test R2 = 0.09
	H2_yield	Train R2 = 0.49, Test R2 = −2.28	Train R2 = 0.49, Test R2 = −2.28
	CO_yield	Train R2 = 0.48, Test R2 = −1.68	Train R2 = 0.48, Test R2 = −1.68
Ridge	CH4_conversion	Train R2 = 0.55, Test R2 = 0.34	Train R2 = 0.55, Test R2 = 0.34
	CO2_conversion	Train R2 = 0.60, Test R2 = 0.21	Train R2 = 0.60, Test R2 = 0.11
	H2_yield	Train R2 = 0.49, Test R2 = −2.28	Train R2 = 0.49, Test R2 = −2.24
	CO_yield	Train R2 = 0.48, Test R2 = −1.65	Train R2 = 0.48, Test R2 = −1.65
Lasso	CH4_conversion	Train R2 = 0.54, Test R2 = 0.48	Train R2 = 0.54, Test R2 = 0.48
	CO2_conversion	Train R2 = 0.60, Test R2 = 0.34	Train R2 = 0.60, Test R2 = 0.34
	H2_yield	Train R2 = 0.49, Test R2 = −2.16	Train R2 = 0.49, Test R2 = −2.16
	CO_yield	Train R2 = 0.48, Test R2 = −1.59	Train R2 = 0.48, Test R2 = −1.59
ElasticNet	CH4_conversion	Train R2 = 0.55, Test R2 = 0.44	Train R2 = 0.55, Test R2 = 0.44
	CO2_conversion	Train R2 = 0.60, Test R2 = 0.24	Train R2 = 0.60, Test R2 = 0.31
	H2_yield	Train R2 = 0.49, Test R2 = −1.81	Train R2 = 0.49, Test R2 = −1.81
	CO_yield	Train R2 = 0.47, Test R2 = −1.31	Train R2 = 0.47, Test R2 = −1.31
Bayesian Ridge	CH4_conversion	Train R2 = 0.54, Test R2 = 0.49	Train R2 = 0.54, Test R2 = 0.49
	CO2_conversion	Train R2 = 0.60, Test R2 = 0.33	Train R2 = 0.60, Test R2 = 0.33
	H2_yield	Train R2 = 0.48, Test R2 = −1.16	Train R2 = 0.48, Test R2 = −1.16
	CO_yield	Train R2 = 0.46, Test R2 = −0.75	Train R2 = 0.46, Test R2 = −0.75
Random Forest	CH4_conversion	Train R2 = 0.93, Test R2 = 0.79	Train R2 = 0.91, Test R2 = 0.76
	CO2_conversion	Train R2 = 0.93, Test R2 = 0.77	Train R2 = 0.94, Test R2 = 0.72
	H2_yield	Train R2 = 0.91, Test R2 = 0.69	Train R2 = 0.93, Test R2 = 0.72
	CO_yield	Train R2 = 0.91, Test R2 = −0.22	Train R2 = 0.92, Test R2 = 0.46
Gradient Boosting	CH4_conversion	Train R2 = 0.50, Test R2 = 0.66	Train R2 = 0.74, Test R2 = 0.76
	CO2_conversion	Train R2 = 0.52, Test R2 = 0.70	Train R2 = 0.91, Test R2 = 0.73
	H2_yield	Train R2 = 1.00, Test R2 = 0.61	Train R2 = 0.61, Test R2 = −0.05
	CO_yield	Train R2 = 0.62, Test R2 = 0.21	Train R2 = 0.62, Test R2 = 0.21
Extra Trees	CH4_conversion	Train R2 = 1.00, Test R2 = −0.66	Train R2 = 1.00, Test R2 = −0.87
	CO2_conversion	Train R2 = 1.00, Test R2 = −1.04	Train R2 = 1.00, Test R2 = −1.02
	H2_yield	Train R2 = 1.00, Test R2 = 0.44	Train R2 = 1.00, Test R2 = 0.86
	CO_yield	Train R2 = 1.00, Test R2 = −0.03	Train R2 = 1.00, Test R2 = 0.10
SVR	CH4_conversion	Train R2 = 0.52, Test R2 = 0.87	Train R2 = 0.52, Test R2 = 0.87
	CO2_conversion	Train R2 = 0.49, Test R2 = 0.93	Train R2 = 0.49, Test R2 = 0.93
	H2_yield	Train R2 = 0.50, Test R2 = 0.55	Train R2 = 0.50, Test R2 = 0.55
	CO_yield	Train R2 = 0.43, Test R2 = 0.82	Train R2 = 0.43, Test R2 = 0.82
NuSVR	CH4_conversion	Train R2 = 0.57, Test R2 = 0.98	Train R2 = 0.51, Test R2 = 0.87
	CO2_conversion	Train R2 = 0.48, Test R2 = 0.92	Train R2 = 0.48, Test R2 = 0.92
	H2_yield	Train R2 = 0.51, Test R2 = 0.68	Train R2 = 0.51, Test R2 = 0.68
	CO_yield	Train R2 = 0.46, Test R2 = 0.76	Train R2 = 0.46, Test R2 = 0.76
Kernel Ridge	CH4_conversion	Train R2 = 0.83, Test R2 = 0.29	Train R2 = 0.83, Test R2 = 0.29
	CO2_conversion	Train R2 = 0.84, Test R2 = 0.10	Train R2 = 0.84, Test R2 = 0.10
	H2_yield	Train R2 = 0.81, Test R2 = −2.81	Train R2 = 0.81, Test R2 = −2.81
	CO_yield	Train R2 = 0.80, Test R2 = −2.49	Train R2 = 0.80, Test R2 = −2.49
XGBoost	CH4_conversion	Train R2 = 0.69, Test R2 = 0.65	Train R2 = 1.00, Test R2 = 0.42
	CO2_conversion	Train R2 = 1.00, Test R2 = 0.16	Train R2 = 1.00, Test R2 = 0.16
	H2_yield	Train R2 = 1.00, Test R2 = 0.33	Train R2 = 0.50, Test R2 = 0.02
	CO_yield	Train R2 = 1.00, Test R2 = 0.07	Train R2 = 0.49, Test R2 = 0.17
LightGBM	CH4_conversion	Train R2 = 0.00, Test R2 = −0.12	Train R2 = 0.00, Test R2 = −0.12
	CO2_conversion	Train R2 = 0.00, Test R2 = −0.18	Train R2 = 0.00, Test R2 = −0.18
	H2_yield	Train R2 = 0.00, Test R2 = −0.79	Train R2 = 0.00, Test R2 = −0.79
	CO_yield	Train R2 = −0.00, Test R2 = −0.93	Train R2 = −0.00, Test R2 = −0.93
CatBoost	CH4_conversion	Train R2 = 0.99, Test R2 = 0.91	Train R2 = 0.91, Test R2 = 0.91
	CO2_conversion	Train R2 = 0.92, Test R2 = 0.87	Train R2 = 0.92, Test R2 = 0.87
	H2_yield	Train R2 = 1.00, Test R2 = 0.67	Train R2 = 0.93, Test R2 = 0.85
	CO_yield	Train R2 = 1.00, Test R2 = 0.77	Train R2 = 0.93, Test R2 = 0.79
MLP Regressor	CH4_conversion	Train R2 = 0.98, Test R2 = 0.39	Train R2 = 0.80, Test R2 = −0.12
	CO2_conversion	Train R2 = 0.82, Test R2 = −0.16	Train R2 = 0.82, Test R2 = −0.44
	H2_yield	Train R2 = 0.76, Test R2 = −4.79	Train R2 = 0.76, Test R2 = −4.84
	CO_yield	Train R2 = 0.75, Test R2 = −4.03	Train R2 = 0.75, Test R2 = −4.10

and

Table A3. Regression models, best parameters (for Grid Search).

CH4 Conversion
Feature Type	Model	Parameters
Original	Linear Regression	{}
Original	Ridge Regression	{‘alphas’: 1.0}
Original	Lasso Regression	{‘alphas’: [1.0 × 10−3, 1.0 × 10−2, 1.0 × 10−1, 1.0 × 100, 1.0 × 101, 1.0 × 102, 1.0 × 103]}
Original	ElasticNet	{‘alphas’: [1.0 × 10−3, 1.0 × 10−2, 1.0 × 10−1, 1.0 × 100, 1.0 × 101, 1.0 × 102, 1.0 × 103], ‘l1_ratio’: 0.1}
Original	Bayesian Ridge	{‘alpha_1’: 0.001, ‘alpha_2’: 1 × 10−6, ‘lambda_1’: 1 × 10−6, ‘lambda_2’: 0.001}
Original	Random Forest	{‘max_depth’: None, ‘n_estimators’: 100}
Original	Gradient Boosting	{‘learning_rate’: 0.01, ‘n_estimators’: 100}
Original	Extra Trees	{‘max_depth’: None, ‘n_estimators’: 100}
Original	SVR	{‘C’: 10, ‘gamma’: ‘scale’}
Original	NuSVR	{‘C’: 10, ‘nu’: 0.9}
Original	Kernel Ridge	{‘alpha’: 0.1, ‘gamma’: 0.1}
Original	XGBoost	{‘learning_rate’: 1, ‘n_estimators’: 50}
Original	LightGBM	{‘learning_rate’: 0.01, ‘n_estimators’: 50}
Original	CatBoost	{‘iterations’: 50, ‘learning_rate’: 0.1}
Original	MLP Regressor	{‘activation’: ‘relu’, ‘alpha’: 0.01, ‘batch_size’: 32, ‘hidden_layer_sizes’: (100,), ‘solver’: ‘adam’}
Poly	Linear Regression	{}
Poly	Ridge Regression	{‘alphas’: 1000.0}
Poly	Lasso Regression	{‘alphas’: [1.0 × 10−3, 1.0 × 10−2, 1.0 × 10−1, 1.0 × 100, 1.0 × 101, 1.0 × 102, 1.0 × 103]}
Poly	ElasticNet	{‘alphas’: [1.0 × 10−3, 1.0 × 10−2, 1.0 × 10−1, 1.0 × 100, 1.0 × 101, 1.0 × 102, 1.0 × 103], ‘l1_ratio’: 0.1}
Poly	Bayesian Ridge	{‘alpha_1’: 0.001, ‘alpha_2’: 1 × 10−6, ‘lambda_1’: 1 × 10−6, ‘lambda_2’: 0.001}
Poly	Random Forest	{‘max_depth’: 20, ‘n_estimators’: 100}
Poly	Gradient Boosting	{‘learning_rate’: 0.01, ‘n_estimators’: 200}
Poly	Extra Trees	{‘max_depth’: None, ‘n_estimators’: 50}
Poly	SVR	{‘C’: 10, ‘gamma’: ‘scale’}
Poly	NuSVR	{‘C’: 10, ‘nu’: 0.9}
Poly	Kernel Ridge	{‘alpha’: 0.1, ‘gamma’: 0.1}
Poly	XGBoost	{‘learning_rate’: 0.01, ‘n_estimators’: 200}
Poly	LightGBM	{‘learning_rate’: 0.01, ‘n_estimators’: 50}
Poly	CatBoost	{‘iterations’: 200, ‘learning_rate’: 1}
Poly	MLP Regressor	{‘activation’: ‘logistic’, ‘alpha’: 0.01, ‘batch_size’: 128, ‘hidden_layer_sizes’: (100, 50), ‘solver’: ‘adam’}
CO2 Conversion
Original	Linear Regression	{}
Original	Ridge Regression	{‘alphas’: 0.1}
Original	Lasso Regression	{‘alphas’: [1.0 × 10−3, 1.0 × 10−2, 1.0 × 10−1, 1.0 × 100, 1.0 × 101, 1.0 × 102, 1.0 × 103]}
Original	ElasticNet	{‘alphas’: [1.0 × 10−3, 1.0 × 10−2, 1.0 × 10−1, 1.0 × 100, 1.0 × 101, 1.0 × 102, 1.0 × 103], ‘l1_ratio’: 0.1}
Original	Bayesian Ridge	{‘alpha_1’: 0.001, ‘alpha_2’: 1 × 10−6, ‘lambda_1’: 1 × 10−6, ‘lambda_2’: 0.001}
Original	Random Forest	{‘max_depth’: 20, ‘n_estimators’: 100}
Original	Gradient Boosting	{‘learning_rate’: 0.01, ‘n_estimators’: 200}
Original	Extra Trees	{‘max_depth’: None, ‘n_estimators’: 50}
Original	SVR	{‘C’: 10, ‘gamma’: ‘scale’}
Original	NuSVR	{‘C’: 10, ‘nu’: 0.9}
Original	Kernel Ridge	{‘alpha’: 0.1, ‘gamma’: 0.1}
Original	XGBoost	{‘learning_rate’: 1, ‘n_estimators’: 50}
Original	LightGBM	{‘learning_rate’: 0.01, ‘n_estimators’: 50}
Original	CatBoost	{‘iterations’: 50, ‘learning_rate’: 0.1}
Original	MLP Regressor	{‘activation’: ‘relu’, ‘alpha’: 0.001, ‘batch_size’: 64, ‘hidden_layer_sizes’: (100,), ‘solver’: ‘adam’}
Poly	Linear Regression	{}
Poly	Ridge Regression	{‘alphas’: 1000.0}
Poly	Lasso Regression	{‘alphas’: [1.0 × 10−3, 1.0 × 10−2, 1.0 × 10−1, 1.0 × 100, 1.0 × 101, 1.0 × 102, 1.0 × 103]}
Poly	ElasticNet	{‘alphas’: [1.0 × 10−3, 1.0 × 10−2, 1.0 × 10−1, 1.0 × 100, 1.0 × 101, 1.0 × 102, 1.0 × 103], ‘l1_ratio’: 0.5}
Poly	Bayesian Ridge	{‘alpha_1’: 0.001, ‘alpha_2’: 1 × 10−6, ‘lambda_1’: 1 × 10−6, ‘lambda_2’: 0.001}
Poly	Random Forest	{‘max_depth’: 10, ‘n_estimators’: 50}
Poly	Gradient Boosting	{‘learning_rate’: 0.1, ‘n_estimators’: 100}
Poly	Extra Trees	{‘max_depth’: 20, ‘n_estimators’: 50}
Poly	SVR	{‘C’: 1, ‘gamma’: ‘scale’}
Poly	NuSVR	{‘C’: 10, ‘nu’: 0.9}
Poly	Kernel Ridge	{‘alpha’: 0.1, ‘gamma’: 0.1}
Poly	XGBoost	{‘learning_rate’: 0.01, ‘n_estimators’: 200}
Poly	LightGBM	{‘learning_rate’: 0.01, ‘n_estimators’: 50}
Poly	CatBoost	{‘iterations’: 200, ‘learning_rate’: 0.1}
Poly	MLP Regressor	{‘activation’: ‘logistic’, ‘alpha’: 0.001, ‘batch_size’: 64, ‘hidden_layer_sizes’: (100, 50), ‘solver’: ‘adam’}
H2 Yield
Original	Linear Regression	{}
Original	Ridge Regression	{‘alphas’: 0.1}
Original	Lasso Regression	{‘alphas’: [1.0 × 10−3, 1.0 × 10−2, 1.0 × 10−1, 1.0 × 100, 1.0 × 101, 1.0 × 102, 1.0 × 103]}
Original	ElasticNet	{‘alphas’: [1.0 × 10−3, 1.0 × 10−2, 1.0 × 10−1, 1.0 × 100, 1.0 × 101, 1.0 × 102, 1.0 × 103], ‘l1_ratio’: 0.5}
Original	Bayesian Ridge	{‘alpha_1’: 0.001, ‘alpha_2’: 1 × 10−6, ‘lambda_1’: 1 × 10−6, ‘lambda_2’: 0.001}
Original	Random Forest	{‘max_depth’: 20, ‘n_estimators’: 50}
Original	Gradient Boosting	{‘learning_rate’: 0.01, ‘n_estimators’: 50}
Original	Extra Trees	{‘max_depth’: 10, ‘n_estimators’: 50}
Original	SVR	{‘C’: 10, ‘gamma’: ‘scale’}
Original	NuSVR	{‘C’: 10, ‘nu’: 0.5}
Original	Kernel Ridge	{‘alpha’: 0.1, ‘gamma’: 0.1}
Original	XGBoost	{‘learning_rate’: 0.01, ‘n_estimators’: 50}
Original	LightGBM	{‘learning_rate’: 0.01, ‘n_estimators’: 50}
Original	CatBoost	{‘iterations’: 50, ‘learning_rate’: 0.1}
Original	MLP Regressor	{‘activation’: ‘relu’, ‘alpha’: 0.001, ‘batch_size’: 64, ‘hidden_layer_sizes’: (100,), ‘solver’: ‘adam’}
Poly	Linear Regression	{}
Poly	Ridge Regression	{‘alphas’: 1000.0}
Poly	Lasso Regression	{‘alphas’: [0.001, 0.01, 0.1, 1.0, 10.0, 100.0, 1000.0]}
Poly	ElasticNet	{‘alphas’: [0.001, 0.01, 0.1, 1.0, 10.0, 100.0, 1000.0], ‘l1_ratio’: 0.1}
Poly	Bayesian Ridge	{‘alpha_1’: 0.001, ‘alpha_2’: 1 × 10−6, ‘lambda_1’: 1 × 10−6, ‘lambda_2’: 0.001}
Poly	Random Forest	{‘max_depth’: 10, ‘n_estimators’: 50}
Poly	Gradient Boosting	{‘learning_rate’: 0.01, ‘n_estimators’: 50}
Poly	Extra Trees	{‘max_depth’: 20, ‘n_estimators’: 50}
Poly	SVR	{‘C’: 10, ‘gamma’: ‘scale’}
Poly	NuSVR	{‘C’: 10, ‘nu’: 0.9}
Poly	Kernel Ridge	{‘alpha’: 0.1, ‘gamma’: 0.1}
Poly	XGBoost	{‘learning_rate’: 0.01, ‘n_estimators’: 50}
Poly	LightGBM	{‘learning_rate’: 0.01, ‘n_estimators’: 50}
Poly	CatBoost	{‘iterations’: 200, ‘learning_rate’: 0.1}
Poly	MLP Regressor	{‘activation’: ‘logistic’, ‘alpha’: 0.001, ‘batch_size’: 128, ‘hidden_layer_sizes’: (100, 100, 50), ‘solver’: ‘adam’}
CO Yield
Original	Linear Regression	{}
Original	Ridge Regression	{‘alphas’: 0.1}
Original	Lasso Regression	{‘alphas’: [1.0 × 10−3, 1.0 × 10−2, 1.0 × 10−1, 1.0 × 100, 1.0 × 101, 1.0 × 102, 1.0 × 103]}
Original	ElasticNet	{‘alphas’: [1.0 × 10−3, 1.0 × 10−2, 1.0 × 10−1, 1.0 × 100, 1.0 × 101, 1.0 × 102, 1.0 × 103], ‘l1_ratio’: 0.5}
Original	Bayesian Ridge	{‘alpha_1’: 0.001, ‘alpha_2’: 1 × 10−6, ‘lambda_1’: 1 × 10−6, ‘lambda_2’: 0.001}
Original	Random Forest	{‘max_depth’: None, ‘n_estimators’: 50}
Original	Gradient Boosting	{‘learning_rate’: 0.01, ‘n_estimators’: 50}
Original	Extra Trees	{‘max_depth’: 10, ‘n_estimators’: 200}
Original	SVR	{‘C’: 10, ‘gamma’: ‘scale’}
Original	NuSVR	{‘C’: 10, ‘nu’: 0.5}
Original	Kernel Ridge	{‘alpha’: 0.1, ‘gamma’: 0.1}
Original	XGBoost	{‘learning_rate’: 0.01, ‘n_estimators’: 50}
Original	LightGBM	{‘learning_rate’: 0.01, ‘n_estimators’: 50}
Original	CatBoost	{‘iterations’: 50, ‘learning_rate’: 0.1}
Original	MLP Regressor	{‘activation’: ‘relu’, ‘alpha’: 0.001, ‘batch_size’: 64, ‘hidden_layer_sizes’: (100,), ‘solver’: ‘adam’}
Poly	Linear Regression	{}
Poly	Ridge Regression	{‘alphas’: 1000.0}
Poly	Lasso Regression	{‘alphas’: [0.001, 0.01, 0.1, 1.0, 10.0, 100.0, 1000.0]}
Poly	ElasticNet	{‘alphas’: [0.001, 0.01, 0.1, 1.0, 10.0, 100.0, 1000.0], ‘l1_ratio’: 0.5}
Poly	Bayesian Ridge	{‘alpha_1’: 0.001, ‘alpha_2’: 1 × 10−6, ‘lambda_1’: 1 × 10−6, ‘lambda_2’: 0.001}
Poly	Random Forest	{‘max_depth’: 20, ‘n_estimators’: 50}
Poly	Gradient Boosting	{‘learning_rate’: 0.01, ‘n_estimators’: 50}
Poly	Extra Trees	{‘max_depth’: None, ‘n_estimators’: 100}
Poly	SVR	{‘C’: 10, ‘gamma’: ‘scale’}
Poly	NuSVR	{‘C’: 10, ‘nu’: 0.9}
Poly	Kernel Ridge	{‘alpha’: 0.1, ‘gamma’: 0.1}
Poly	XGBoost	{‘learning_rate’: 0.01, ‘n_estimators’: 100}
Poly	LightGBM	{‘learning_rate’: 0.01, ‘n_estimators’: 50}
Poly	CatBoost	{‘iterations’: 200, ‘learning_rate’: 0.1}
Poly	MLP Regressor	{‘activation’: ‘logistic’, ‘alpha’: 0.0001, ‘batch_size’: 32, ‘hidden_layer_sizes’: (100, 100, 50), ‘solver’: ‘adam’}

—Appendix C), enhancing model generalizability and reducing overfitting. Evaluation based on R² and MSE for both train/test datasets indicated that CatBoost and Gradient Boosting consistently outperformed others.

3.3.2. Prediction Results

Fifteen regression models, including linear, regularized, ensemble, kernel-based, and neural network methods, were optimized using GridSearchCV and validated with LOOCV. Hyperparameters were tuned for each model to balance complexity and accuracy. Ensemble models (e.g., Random Forest, Gradient Boosting, CatBoost) demonstrated strong performance in capturing DRM non-linearities. Key parameters (e.g., estimators, depth, learning rate) were optimized for predictive efficiency. Models were assessed using R² and MSE to identify optimal predictors for each output. The findings guide selection of models balancing interpretability and performance in catalytic process modelling.

3.3.3. Cross-Validation Comparison (CV = 3 vs. CV = 5)

Compared to 3-fold cross-validation, CV = 5 produced more stable performance estimates, particularly by reducing variance. Models such as Ridge, Lasso, and ElasticNet maintained consistent R² values across folds, indicating reliability. In contrast, Extra Trees and LightGBM exhibited signs of overfitting, with high training R² but poor generalization on test data—especially under CV = 3. CatBoost and Random Forest emerged as top performers, consistently achieving high test R² across all folds, demonstrating strong generalizability.

3.3.4. Best Hyperparameters

Key hyperparameters identified through GridSearchCV are summarized in Table A3, highlighting the optimal configurations for each target variable. For CH₄ conversion, CatBoost performed best on the original dataset with 50 iterations and a learning rate of 0.1, while Gradient Boosting on the polynomial-transformed data used a 0.01 learning rate and 200 estimators. CO₂ conversion was optimized using CatBoost with 200 iterations and a 0.1 learning rate on the polynomial dataset, and Gradient Boosting with a 0.1 rate and 100 estimators. For H₂ yield, Random Forest on the original dataset achieved strong results with 50 estimators and a maximum depth of 20, whereas CatBoost on the polynomial dataset used 200 iterations and a 0.1 learning rate. CO yield was best predicted using CatBoost (200 iterations, 0.1 rate) and Gradient Boosting (0.01 rate, 50 estimators) on the polynomial dataset. These hyperparameter settings effectively balanced model complexity and learning efficiency, leading to improved prediction accuracy across all targets.

3.3.5. Model Performance and Evaluation Metrics

When evaluated on the test data, model performances varied considerably, as shown in Figure 4, Figure 5, Figure 6 and Figure 7. Model performance across the four DRM targets—CH₄ conversion, CO₂ conversion, H₂ yield, and CO yield—is summarized in

Table 5. Regression model Metrics (R2 and MSE values) for original and polynomial features CV = 5.

CH4 Conversion
Features	Model	Train R2	Test R2	Train MSE	Test MSE
Original	Linear Regression	0.55	0.24	184.20	102.13
Original	Ridge Regression	0.55	0.34	184.61	88.90
Original	Lasso Regression	0.54	0.48	187.41	70.35
Original	ElasticNet	0.55	0.44	186.00	76.15
Original	Bayesian Ridge	0.54	0.49	187.31	69.21
Original	Random Forest	0.93	0.84	27.17	21.54
Original	Gradient Boosting	0.74	0.76	108.07	31.99
Original	Extra Trees	1.00	−1.00	0.00	270.33
Original	SVR	0.52	0.87	199.66	17.89
Original	NuSVR	0.51	0.87	199.68	18.22
Original	Kernel Ridge	0.83	0.29	69.08	96.55
Original	XGBoost	1.00	0.42	0.00	79.08
Original	LightGBM	0.00	−0.12	411.68	151.17
Original	CatBoost	0.91	0.91	35.57	12.19
Original	MLP Regressor	0.81	−0.03	76.24	139.37
Poly	Linear Regression	0.82	−0.01	72.95	136.13
Poly	Ridge Regression	0.59	0.43	168.40	77.64
Poly	Lasso Regression	0.77	0.66	94.02	46.37
Poly	ElasticNet	0.77	0.61	94.60	52.83
Poly	Bayesian Ridge	0.57	0.31	178.06	92.65
Poly	Random Forest	0.92	0.93	33.16	9.29
Poly	Gradient Boosting	0.95	0.94	19.82	7.58
Poly	Extra Trees	1.00	−0.27	0.00	171.21
Poly	SVR	−0.03	0.24	423.73	102.40
Poly	NuSVR	−0.07	0.18	441.99	111.03
Poly	Kernel Ridge	0.96	−8.94	15.82	1344.17
Poly	XGBoost	0.93	0.64	28.00	48.13
Poly	LightGBM	0.00	−0.12	411.68	151.17
Poly	CatBoost	1.00	0.93	0.00	9.80
Poly	MLP Regressor	−0.23	−0.24	505.51	167.62
CO2 Conversion
Original	Linear Regression	0.60	0.09	167.62	124.03
Original	Ridge Regression	0.60	0.11	167.63	122.36
Original	Lasso Regression	0.60	0.34	170.83	89.60
Original	ElasticNet	0.60	0.31	169.64	93.78
Original	Bayesian Ridge	0.60	0.33	169.90	92.09
Original	Random Forest	0.91	0.80	38.10	27.30
Original	Gradient Boosting	0.91	0.73	38.84	36.99
Original	Extra Trees	1.00	−0.79	0.00	244.22
Original	SVR	0.49	0.93	217.72	10.18
Original	NuSVR	0.48	0.92	218.40	10.64
Original	Kernel Ridge	0.84	0.10	69.31	122.58
Original	XGBoost	1.00	0.16	0.00	114.28
Original	LightGBM	0.00	−0.18	423.91	161.43
Original	CatBoost	0.92	0.87	32.89	17.74
Original	MLP Regressor	0.81	−0.23	80.68	167.99
Poly	Linear Regression	0.84	−0.26	67.26	172.18
Poly	Ridge Regression	0.64	0.28	152.92	98.17
Poly	Lasso Regression	0.78	0.58	92.40	58.05
Poly	ElasticNet	0.79	0.55	89.94	61.13
Poly	Bayesian Ridge	0.62	0.14	161.32	117.54
Poly	Random Forest	0.93	0.96	31.62	5.74
Poly	Gradient Boosting	1.00	0.99	1.00	1.99
Poly	Extra Trees	1.00	−0.42	0.00	194.76
Poly	SVR	−0.09	0.01	463.14	135.56
Poly	NuSVR	−0.12	0.12	472.79	120.34
Poly	Kernel Ridge	0.97	−7.22	14.45	1124.21
Poly	XGBoost	0.93	0.76	27.73	32.49
Poly	LightGBM	0.00	−0.18	423.91	161.43
Poly	CatBoost	1.00	1.00	0.01	0.57
Poly	MLP Regressor	−0.10	−0.01	464.30	138.71
H2 Yield
Original	Linear Regression	0.49	−2.28	133.81	105.28
Original	Ridge Regression	0.49	−2.24	133.81	104.06
Original	Lasso Regression	0.49	−2.16	133.84	101.33
Original	ElasticNet	0.49	−1.81	134.25	90.20
Original	Bayesian Ridge	0.48	−1.16	136.73	69.42
Original	Random Forest	0.91	0.88	23.73	3.72
Original	Gradient Boosting	0.61	−0.05	103.63	33.78
Original	Extra Trees	1.00	0.81	0.00	6.24
Original	SVR	0.50	0.55	130.97	14.49
Original	NuSVR	0.51	0.68	129.58	10.16
Original	Kernel Ridge	0.81	−2.81	49.93	122.31
Original	XGBoost	0.50	0.02	132.17	31.30
Original	LightGBM	0.00	−0.79	262.74	57.36
Original	CatBoost	0.93	0.85	18.12	4.67
Original	MLP Regressor	0.76	−4.82	62.78	186.81
Poly	Linear Regression	0.78	−4.14	56.55	164.95
Poly	Ridge Regression	0.54	−1.76	121.50	88.58
Poly	Lasso Regression	0.76	−2.14	63.15	100.70
Poly	ElasticNet	0.70	−0.79	78.14	57.43
Poly	Bayesian Ridge	0.51	−2.11	128.03	99.75
Poly	Random Forest	0.91	0.66	22.37	10.80
Poly	Gradient Boosting	0.61	0.23	103.33	24.87
Poly	Extra Trees	1.00	0.31	0.00	22.13
Poly	SVR	−0.01	0.48	266.67	16.58
Poly	NuSVR	−0.03	0.48	271.37	16.73
Poly	Kernel Ridge	0.97	−10.79	6.79	378.17
Poly	XGBoost	0.50	0.19	131.38	25.90
Poly	LightGBM	0.00	−0.79	262.74	57.36
Poly	CatBoost	1.00	0.84	0.00	5.17
Poly	MLP Regressor	−0.00	−0.55	263.42	49.74
CO Yield
Original	Linear Regression	0.48	−1.68	138.31	97.79
Original	Ridge Regression	0.48	−1.65	138.31	96.69
Original	Lasso Regression	0.48	−1.59	138.34	94.21
Original	ElasticNet	0.47	−1.31	138.74	84.13
Original	Bayesian Ridge	0.46	−0.75	141.53	63.83
Original	Random Forest	0.89	−0.00	29.68	36.56
Original	Gradient Boosting	0.62	0.21	101.32	28.90
Original	Extra Trees	1.00	−0.34	0.00	48.71
Original	SVR	0.43	0.82	151.50	6.67
Original	NuSVR	0.46	0.76	141.57	8.64
Original	Kernel Ridge	0.80	−2.49	51.58	127.00
Original	XGBoost	0.49	0.17	133.45	30.14
Original	LightGBM	−0.00	−0.93	263.63	70.22
Original	CatBoost	0.93	0.79	17.65	7.64
Original	MLP Regressor	0.74	−3.86	68.31	177.14
Poly	Linear Regression	0.77	−3.67	59.74	170.11
Poly	Ridge Regression	0.52	−1.35	127.32	85.69
Poly	Lasso Regression	0.68	−0.43	83.09	52.07
Poly	ElasticNet	0.69	−0.46	81.68	53.16
Poly	Bayesian Ridge	0.50	−1.54	132.34	92.41
Poly	Random Forest	0.89	0.13	27.96	31.82
Poly	Gradient Boosting	0.61	0.11	102.21	32.43
Poly	Extra Trees	1.00	−0.92	0.00	70.13
Poly	SVR	−0.05	0.33	277.53	24.40
Poly	NuSVR	−0.07	0.33	281.13	24.33
Poly	Kernel Ridge	0.97	−9.72	7.19	390.50
Poly	XGBoost	0.75	0.50	66.91	18.17
Poly	LightGBM	−0.00	−0.93	263.63	70.22
Poly	CatBoost	1.00	0.89	0.01	3.97
Poly	MLP Regressor	−0.00	−0.63	264.70	59.26

and Figure 4, Figure 5, Figure 6 and Figure 7. Ensemble-based methods such as Random Forest and Gradient Boosting consistently produced predictions closest to the ideal line, reflecting their ability to capture nonlinear relationships in small datasets. In contrast, simpler linear models (e.g., Ridge, Lasso) exhibited greater scatter, particularly at the extremes of the observed range, indicating limitations in modeling complex interactions. Presenting the models together in these figures allows a direct, side-by-side visual comparison of predictive accuracy, highlighting both absolute performance and relative strengths across modeling approaches.

CatBoost on the original dataset achieved strong results for CH₄ conversion (R² = 0.91, MSE = 12.19), while Gradient Boosting with polynomial features performed slightly better (R² = 0.94, MSE = 7.58). This is comparable to the results reported using ANN-MLP (Multi-layer Perceptron) with R² = 0.96 and ANN-RBF (Radial Basis Function) with R² = 0.83 [7]. For CO₂ conversion, CatBoost with polynomial features delivered near-perfect accuracy (R² = 1.00, MSE = 0.57), underscoring the value of feature transformation. This is comparable to ANN-MLP (R² = 0.94) and ANN-RBF (R² = 0.74) [7].

Random Forest excelled in predicting H₂ yield (R² = 0.88, MSE = 3.72), with CatBoost close behind (R² = 0.84, MSE = 5.17). This is comparable to ANN-MLP (R² = 0.97) and ANN-RBF (R² = 0.92) [7]. In predicting CO yield, CatBoost again led (R² = 0.89, MSE = 3.97), while Gradient Boosting on the original dataset underperformed (R² = 0.21). This is comparable to ANN-MLP (R² = 0.85) and ANN-RBF (R² = 0.78) [7].

To ensure a fair comparison, we reimplemented the ANN-MLP and ANN-RBF models described by Hossain et al. [7] using the same dataset and a 70:30 train-test split. The resulting R² values on the test set were substantially lower: for ANN-MLP, R² = −0.99 (H₂ yield), −1.03 (CO yield), −0.12 (CH₄ conversion), and –0.08 (CO₂ conversion); and for ANN-RBF, R² = −2.91 (H₂ yield), −3.47 (CO yield), −2.55 (CH₄ conversion), and −2.26 (CO₂ conversion). These results indicate poor generalization performance and suggest that the original study likely reported metrics based on training or full datasets.

Parity plots for the reimplemented ANN models (Figure 8) further illustrate the discrepancy between predicted and observed values on test data. These results demonstrate limited generalization performance in the earlier study compared to the models developed in this study.

In contrast, the models developed in this study—particularly CatBoost and Gradient Boosting—demonstrated consistently high R² values across all targets on the test set, confirming their robustness and generalizability. In several cases, CatBoost predictions closely matched experimental values with minimal error. For example:

At 800 °C, CH₄/CO₂ = 1.0, Ni loading = 5 wt.%, experimental CH₄ conversion was 67.93%, CatBoost predicted 68.00% (absolute error 0.07%).

At 800 °C, CH₄/CO₂ = 0.4, Ni loading = 15 wt.%, experimental CO₂ conversion was 30.02%, CatBoost predicted 30.00% (absolute error 0.02%).

At 750 °C, CH₄/CO₂ = 1.0, Ni loading = 10 wt.%, experimental H₂ yield was 21.11%, CatBoost predicted 21.00% (absolute error 0.11%).

At 750 °C, CH₄/CO₂ = 0.7, Ni loading = 10 wt.%, experimental CO yield was 15.06%, CatBoost predicted 15.00% (absolute error 0.06%).

These results highlight the importance of model selection, feature engineering, and rigorous validation. Overall, CatBoost consistently performed well across all targets due to its ability to capture complex interactions, while Gradient Boosting and Random Forest also showed strong generalizability. SVR and NuSVR captured non-linear trends but were prone to overfitting with polynomial features, emphasizing the need to align model complexity with data characteristics.

3.3.6. Leave-One-Out Cross-Validation (LOOCV) Results

Given the small dataset (n = 27), LOOCV was employed for a granular evaluation of model generalizability. Each sample was used once for validation, with the remainder for training. This maximized data utility and minimized bias in performance estimates (

Table 6. LOOCV performance metrics before and after removal of the outliers.

Model	Target	Feature Type	R2 After Removal of Outliers	MSE After Removal of Outliers	R2 Without Removal of Outliers	MSE Without Removal of Outliers
Random Forest	CH4_conversion	Original	0.68	60.79	0.39	232.70
Gradient Boosting	CH4_conversion	Original	0.62	71.44	0.47	203.60
SVR	CH4_conversion	Original	−0.07	201.26	−0.00	383.03
CatBoost	CH4_conversion	Original	0.55	85.05	0.22	296.99
Random Forest	CH4_conversion	Polynomial	0.59	77.48	0.33	256.60
Gradient Boosting	CH4_conversion	Polynomial	0.59	76.47	0.17	317.54
SVR	CH4_conversion	Polynomial	−0.17	221.06	−0.09	415.53
CatBoost	CH4_conversion	Polynomial	0.42	108.88	0.18	314.33
Random Forest	CO2_conversion	Original	0.86	29.20	0.45	216.55
Gradient Boosting	CO2_conversion	Original	0.82	36.19	0.44	222.20
SVR	CO2_conversion	Original	0.01	201.30	−0.04	408.69
CatBoost	CO2_conversion	Original	0.68	65.26	0.26	292.33
Random Forest	CO2_conversion	Polynomial	0.77	46.09	0.40	235.11
Gradient Boosting	CO2_conversion	Polynomial	0.82	36.06	0.16	329.38
SVR	CO2_conversion	Polynomial	−0.06	216.97	−0.10	432.73
CatBoost	CO2_conversion	Polynomial	0.60	81.57	0.25	295.61
Random Forest	H2_yield	Original	0.41	31.20	0.30	168.51
Gradient Boosting	H2_yield	Original	0.31	36.29	0.29	169.16
SVR	H2_yield	Original	0.06	49.88	−0.04	250.12
CatBoost	H2_yield	Original	0.32	35.80	0.21	188.09
Random Forest	H2_yield	Polynomial	0.20	42.47	0.08	220.01
Gradient Boosting	H2_yield	Polynomial	0.15	44.97	0.19	192.93
SVR	H2_yield	Polynomial	−0.09	57.82	−0.12	267.80
CatBoost	H2_yield	Polynomial	0.25	39.93	0.23	183.36
Random Forest	CO_yield	Original	0.69	14.25	0.27	176.98
Gradient Boosting	CO_yield	Original	0.72	12.82	0.27	175.99
SVR	CO_yield	Original	0.10	41.98	−0.02	246.21
CatBoost	CO_yield	Original	0.50	23.03	0.18	197.30
Random Forest	CO_yield	Polynomial	0.45	25.41	0.06	226.24
Gradient Boosting	CO_yield	Polynomial	0.56	20.20	0.09	220.04
SVR	CO_yield	Polynomial	−0.06	49.14	−0.08	261.20
CatBoost	CO_yield	Polynomial	0.41	27.44	0.17	200.38

). Random Forest, Gradient Boosting, SVR, and CatBoost were chosen for LOOCV due to prior strong performance and ability to handle non-linear interactions efficiently.

To evaluate the influence of outliers on model performance, we conducted a sensitivity analysis by comparing predictions generated using the full dataset against those obtained after removing identified outliers. Outliers were detected based on outliers were identified using the Interquartile Range (IQR) method, which indicated data points with disproportionately high prediction errors.

Key Findings:

Figure 9 and Figure 10 illustrate the predicted versus actual values obtained from Leave-One-Out Cross-Validation (LOOCV) for Random Forest and Gradient Boosting models, respectively. Subfigures (a) show model performance on the original dataset including all samples, while subfigures (b) depict the results after removing the outliers.

Outlier removal significantly improved model accuracy, as seen in the Random Forest model for CH₄ conversion, where R² increased from 0.39 to 0.68 (Figure 9a,b and Figure 10a,b), highlighting the importance of data quality. Removal of outliers improved the alignment between predicted and actual values, as seen by tighter clustering around the ideal y = x line, particularly in the Gradient Boosting model (Figure 10b). CatBoost and Gradient Boosting maintained high R² values even in the presence of outliers, demonstrating their robustness. This comparative analysis demonstrates that outlier removal is useful for understanding model sensitivity but was not used as a standard preprocessing step. All primary modelling conclusions were based on the full dataset to maintain data integrity and avoid bias. Polynomial feature transformations generally enhanced model performance, particularly for CatBoost and Gradient Boosting; however, SVR and NuSVR exhibited overfitting when such features were introduced, indicating sensitivity to model complexity.

Advantages of LOOCV:

Advantages of LOOCV include Lower Bias: Almost all data used for training in each iteration and High Sensitivity: Particularly valuable for small datasets, providing detailed performance estimates.

Challenges of LOOCV:

Challenges of LOOCV include Higher Variance: Results may vary due to model sensitivity to minor data changes and Computational Cost: Manageable in this study due to small sample size.

Comparison with GridSearchCV:

While GridSearchCV optimized hyperparameters using CV = 3/5, LOOCV offered detailed model validation. Both approaches together confirmed CatBoost, Gradient Boosting, and Random Forest as optimal for DRM predictions.

Bias-Variance Trade-Off:

Model performance revealed classic bias-variance trade-offs. Models with high variance, such as SVR with polynomial features, tended to overfit the training data, resulting in poor generalization and reduced accuracy on test sets. In contrast, low-bias models like linear regressors demonstrated reasonable accuracy during training but lacked the flexibility to capture the complex, non-linear patterns present in the data. These findings emphasize the importance of balancing model complexity to achieve optimal generalization performance.

To summarise, LOOCV reinforced model selection insights, emphasizing the value of CatBoost and Gradient Boosting for reliable DRM outcome prediction. These models, combined with appropriate feature engineering, offer robust and accurate predictions suitable for real-world applications.

3.3.7. CatBoost Hyperparameter R² Analysis

CatBoost exhibits robust performance, effectively managing complex data relationships, which results in high test R² values. Its built-in regularization techniques mitigate overfitting, promoting strong generalization to unseen data. Hyperparameter interactions, such as between iterations and learning rate, contribute synergistically to performance improvement when optimally combined. (Figure A1, Figure A2, Figure A3, Figure A4, Figure A5, Figure A6, Figure A7 and Figure A8—Appendix D) Illustrate the sensitivity of Mean Test R² to these hyperparameter interactions for both original and polynomial features.

Key Insights:

Model performance was significantly influenced by the interaction of key hyperparameters, particularly the combination of iterations and learning rate. Even when individual contributions appeared modest, their optimal pairing led to substantial performance gains. CatBoost demonstrated a strong ability to capture intricate feature interactions, especially when polynomial features were included, further enhancing predictive accuracy. The relationship between the number of iterations and Mean Test R² was notably non-linear, with performance peaking and then plateauing or declining—an indication of overfitting beyond a certain threshold. For H₂ and CO yield, the optimal number of iterations was observed around 160, after which model performance began to deteriorate. Additionally, the learning rate played a critical role, with values between 0 and 0.2 yielding the most stable and reliable results across different iteration counts. In summary, CatBoost’s high-test R² arises from the interplay of multiple hyperparameters and its inherent strengths. Proper hyperparameter tuning is critical to avoid overfitting and achieve optimal results.

3.3.8. Evaluation of Output Predictions Based on MAE and RMSE

Figure 11, Figure 12, Figure 13 and Figure 14 display MAE and RMSE values for predicting CH₄ Conversion, CO₂ Conversion, H₂ Yield, and CO Yield. These values align with trends in MSE and R², supporting the reliability of model evaluations.

CH₄ Conversion: Linear Regression: MAE = 9.20, RMSE = 10.11 (Original), MAE = 10.69, RMSE = 11.67 (Polynomial). Random Forest: MAE = 5.57, RMSE = 7.31 (Original), MAE = 3.17, RMSE = 3.30 (Polynomial). CatBoost: MAE = 2.52, RMSE = 3.50 (Original), MAE = 3.13, RMSE = 3.13 (Polynomial).

CO₂ Conversion: Similar patterns were observed, with Gradient Boosting and Random Forest showing considerable improvements with polynomial features, while Kernel Ridge and SVR deteriorated.

H₂ Yield: Models like Random Forest and Extra Trees showed significant improvements with polynomial features, while others such as Bayesian Ridge and MLP Regressor showed mixed results. CatBoost performed consistently well without polynomial features.

CO Yield: Polynomial features benefited Random Forest and Gradient Boosting, while SVR, NuSVR, and Kernel Ridge saw adverse effects. Extra Trees and XGBoost showed moderate improvements.

To summarise, MAE and RMSE metrics confirm trends observed in R² and MSE.

Non-linear models such as Random Forest and Gradient Boosting benefit from polynomial features, while linear models often show degraded performance. CatBoost and Gradient Boosting generally outperform other models across various metrics (MAE, RMSE, R², and MSE), indicating strong predictive power and minimal error. LOOCV results further validate these models’ robustness.

4. Model Performance Metrics in DRM: Comparing CH₄ and CO₂ Conversions with H₂ and CO Yields

Model performance metrics reveal that CH₄ and CO₂ conversions generally outperform H₂ and CO yields in DRM reactions. This disparity arises from several factors. The primary DRM reactions involving CH₄ and CO₂ are well-characterized and more straightforward, resulting in consistent conversion outcomes [35]. Catalysts are typically optimized for these conversions, whereas H₂ and CO yields are more susceptible to catalyst deactivation, which can reduce performance [36]. Additionally, the thermodynamic equilibrium of DRM favors CH₄ and CO₂ conversion at elevated temperatures, while H₂ and CO yields are more sensitive to fluctuations in temperature and pressure [39]. Finally, the reaction rates for CH₄ and CO₂ conversion are inherently higher than those for secondary reactions producing H₂ and CO, contributing to the observed differences in predictive accuracy.

5. Parametric Influence, Interactions, and Predictive Insight

Predictions from the top-performing CatBoost and Random Forest models consistently indicated that optimal syngas production—maximizing H₂ and CO yields—occurs when the CH₄/CO₂ feed ratio is near 1.0 and the reaction temperature is between 780–820 °C. These ranges align with well-established DRM operating windows, where sufficient thermal energy sustains the endothermic reaction while maintaining catalyst stability.

Key Variables: Feature importance rankings consistently identified reaction temperature, feed ratio, and Ni metal loading as the dominant factors influencing conversions and yields. Temperature showed the greatest influence, followed by feed ratio and metal loading.

Optimal Ranges and Interactions: Ni loading between 2–4 wt.% was found to positively impact yields, particularly at moderate temperatures. Interaction analysis revealed synergistic effects between feed ratio and temperature, and between temperature and metal loading. For example, slightly lean methane feeds (<1.0) can boost CO₂ conversion at the expense of CH₄ conversion, indicating potential trade-offs depending on desired syngas composition.

Practical Implications: These predictive insights enable rapid screening of promising conditions, allowing experimental efforts to focus on the most effective temperature–feed ratio–loading combinations. This approach is particularly useful in small-data scenarios, providing a data-efficient surrogate for guiding DRM experimentation.

Limitations: The trends reported here are derived from a dataset of 27 points for a single Ni/CaFe₂O₄ catalyst system. While consistent with DRM thermodynamics and literature trends, experimental validation across a wider range of catalysts and conditions is required to generalize these findings.

By translating model outputs into actionable operational guidance, this section bridges machine learning predictions with practical DRM process development.

Based on predictions from CatBoost and Random Forest models, optimal syngas production—defined by maximized H2 and CO yields—was consistently observed when the Feed Ratio approached 1.0 and Reaction Temperature ranged between 780–820 °C. These conditions align with well-established operating windows for dry reforming, where sufficient thermal energy sustains endothermic reforming while preserving catalyst stability. Although visual contour plots are not included in this version, the inferred response trends provide actionable insight into high-performance DRM regimes. However, based on predictions from CatBoost and Random Forest models, we observed that syngas production—defined here by higher H2 and CO yields—was consistently maximized when the Feed Ratio approached 1.0 and Reaction Temperature ranged between 780–820 °C. These conditions align with known optimal windows for dry reforming, where sufficient thermal energy drives endothermic reforming while maintaining catalytic stability. While we reserve detailed graphical visualizations for future or companion study, this quantitative inference provides actionable insight into high-performance DRM settings.

Additionally, interaction terms, particularly Feed Ratio × Reaction Temperature, correlated strongly with output variables (up to 0.70), underscoring synergistic effects between operating conditions. The outputs themselves were highly correlated (0.92–0.99), suggesting concurrent production trends and highlighting the potential for process-wide optimization strategies, indicating that DRM performance is primarily driven by thermal and compositional factors. These results align with previous studies highlighting DRM’s sensitivity to temperature and reactant ratios. Although, separate models were trained for multi-output and parallel single-output, they shared a unified preprocessing and feature engineering pipeline, enabling a multi-output learning framework through systematic coordination. This pragmatic structure reflects how multi-output modelling can be implemented in data-scarce environments without explicit multi-target regressors.

Use of Reinforcement Learning (RL) for multi-objective optimization in chemical processes derive optimal control policies by interacting with simulated environments or digital twins [40,41]. While RL excels in adaptive process control, this study takes a complementary approach by employing supervised learning to develop accurate predictive models for CH₄ and CO₂ conversions and H₂ and CO yields based on experimental data. This predictive framework can serve as a data-efficient surrogate model, offering high-fidelity predictions for RL agents or control optimization algorithms in DRM.

To strengthen model interpretability, especially in the context of polynomial transformations, the study ensured that second-order terms were physically grounded (e.g., Feed Ratio × Temperature reflecting synergistic kinetic effects). The feature transformation pipeline details the interaction terms used and their chemical rationale. For example, the interaction between metal loading and temperature maps onto observed trends in catalyst stability, while Feed Ratio × Temperature captures known dependencies in DRM kinetics and equilibrium. This focus on feature engineering represents a central novelty of this study, particularly given the limited dataset.

Regarding model robustness, the Leave-One-Out Cross-Validation (LOOCV) and GridSearchCV for hyperparameter tuning help balance variance and bias in performance estimates. While LOOCV has inherent high variance, its thoroughness is valuable in small-data settings, and the use of additional test splits ensures that model overfitting is continuously monitored. Similar ML studies using small experimental datasets are reported [42].

6. Novelty and Impact

This study introduces several novel contributions to DRM research. Unlike conventional approaches that focus on single-output predictions, we employ multi-output regression models to simultaneously forecast CH₄ conversion, CO₂ conversion, H₂ yield, and CO yield, enabling process-wide optimization. A comprehensive evaluation of fifteen machine learning models—including linear, ensemble, and Bayesian regressors—was conducted to identify the most accurate predictive framework. Feature transformations, such as polynomial expansions and interaction terms, along with outlier handling, significantly improved model accuracy and interpretability. Outlier analysis further refined model reliability by reducing predictive variance and revealing hidden inconsistencies in the experimental data. Importantly, the study supports low-carbon hydrogen production and contributes to carbon-neutral energy systems, aligning with Sustainable Development Goals 7 and 13. Overall, the findings offer actionable insights for optimizing DRM reactions in industrial settings and provide a robust framework for model selection and process enhancement.

7. Limitations and Future Work

While this study demonstrates the feasibility of using machine learning models for multi-output prediction in DRM, a few limitations remain. First, the dataset comprises only 27 samples from a single catalyst, which constrains model complexity, limits generalizability, and prevents the inclusion of catalyst property parameters known to influence reaction performance. Though LOOCV and GridSearchCV mitigate overfitting, the absence of catalyst descriptors (e.g., surface area, pore size, metal dispersion, chemical composition) represents a key restriction. Future work will focus on expanding the dataset with additional catalysts and their corresponding physicochemical properties, obtained through experimental runs or high-fidelity simulations, enabling integration of these descriptors as predictors. While polynomial feature transformations improved model accuracy, they may introduce interpretability challenges. Although the study emphasizes supervised regression, reinforcement learning and hybrid ML–reaction modelling strategies could further enhance process control and optimization under dynamic conditions.

8. Conclusions

This study demonstrates the effectiveness of various regression models in predicting DRM outcomes. CatBoost and Gradient Boosting consistently performed well, especially with polynomial features. CatBoost’s ability to manage both categorical and numerical data while preventing overfitting was a key strength, while Gradient Boosting’s sequential learning approach also yielded strong results. Random Forest showed robust performance, particularly for H₂ Yield and CO₂ Conversion. SVR and NuSVR effectively captured non-linear relationships but required careful tuning, especially with polynomial features. The study also highlighted the importance of cross-validation techniques, such as LOOCV, for small datasets. By evaluating multiple models and performing detailed outlier analysis, the study provides a comprehensive understanding of predictive modelling for DRM, with practical applications in optimizing reaction parameters for enhanced performance.