Machine Learning-Based Predictive Modeling for Solid Oxide Electrolysis Cell (SOEC) Electrochemical Performance

Abstract

Solid oxide electrolysis cells (SOECs) are emerging as a promising technology for high-efficiency and environmentally friendly hydrogen production. While laboratory-scale experiments and physics-based simulations have significantly advanced SOEC research, there remains a need for faster, scalable, and cost-effective methods to predict electrochemical performance. This study explores the feasibility of using machine learning (ML) techniques to model the performance of SOECs with the material configuration LSM-YSZ/YSZ/Ni-YSZ. A dataset of 593 records (from 31 IV curves) was compiled from 12 peer-reviewed sources and used to train and evaluate four ML algorithms: SVR, ANN, XGBoost, and Random Forest. Among these, XGBoost achieved the highest accuracy, with an R² of 98.39% for cell voltage prediction and 98.10% for IV curve interpolation test under typical conditions. Extrapolation tests revealed the model’s limitations in generalizing beyond the bounds of the training data, emphasizing the importance of comprehensive data coverage. Overall, the results confirm that ML models, particularly XGBoost, can serve as accurate and efficient tools for predicting SOEC electrochemical behavior when applied with appropriate data coverage and guided by materials science concepts.

1. Introduction

Hydrogen, the most abundant gas in the universe, is widely considered the fuel of the future. The hydrogen molecule (H₂) is a light and colorless gas at room temperature that can be produced from various sources such as oil, coal, natural gas, biomass, organic waste, and water [1]. Hydrogen production plays a pivotal role in advancing the sustainability of the energy industry. Hydrogen offers several benefits, such as high energy density, a renewable nature, the ability to serve as a renewable energy carrier, an ease of storage and transport, and clean combustion characteristics [2]. Currently, 96% of hydrogen is produced using fossil fuels. Global decarbonizing efforts are now a priority for the energy industry since the current methods for mass hydrogen production impose several environmental impacts due to the emissions caused during production [3]. Hydrogen is produced through the process of water electrolysis, an electrochemical conversion of water to an almost pure hydrogen gas without detrimental impurities. Water electrolysis technologies are categorized based on their operating conditions and charge carrier types. The four types of electrolysis are (1) alkaline, (2) proton exchange membrane (PEM), (3) anion exchange membrane (AEM), and (4) solid oxide (SOE). Alkaline electrolysis is already a stable and commercially mature technology, with a 62–82% process efficiency. PEM electrolysis is also a commercially available technology that can operate at high current densities with a process efficiency of 67–82%. AEM electrolysis uses a less expensive membrane than PEM electrolysis, but it is still a developing technology with an efficiency estimated at ~40%. Solid oxide electrolysis is currently still a developing technology with the highest potential to achieve technical efficiencies up to 100% [4].

Among these technologies, solid oxide electrolysis cells (or SOECs), are particularly promising to support the drive for sustainable hydrogen production. An SOEC operates at elevated temperatures between 500 °C and 1000 °C, which enhances the ionic conductivity of the electrolyte and lowers the electrical energy demand by utilizing heat as additional input [5]. However, specific challenges also come with high operating temperatures, such as difficulties sealing the electrolytic stack, thermal cycle performance, and electrode degradation for long-term operations [6].

The performance of SOECs is commonly evaluated using current–voltage (IV) or polarization curves. A polarization curve captures the relationship between applied voltage and resulting current density, and it provides information on electrochemical losses and cell efficiency [7]. The polarization behavior of SOECs is influenced by several factors, such as triple-phase boundary (TPB) activity, operating temperature, gas composition and partial pressures, and the microstructure of the cell [8]. For instance, Kim et al. [9] demonstrated that, when steam ratios drop to less than 10%, a dramatic increase in overpotentials is observed at low current densities (<0.2 A/cm²), highlighting the sensitivity of SOECs to inlet gas composition. Similarly, Kupecki et al. [10] reported that the introduction of a pore-forming graphite agent in SOECs with 8YSZ electrolyte increased the open porosity by 2% and resulted in higher current densities, highlighting the role of microstructure in performance optimization.

During the water electrolysis process of SOECs, the water molecule is first reduced into hydrogen (H₂) and oxide ion (O²⁻) at the cathode after the addition of two electrons. Hydrogen is then released outside the cathodic surface while the oxide ion travels to the anode through an ion exchange membrane. The oxide ion is then reduced further to produce oxygen and electrons. Oxygen gas is then released outside the anodic surface while the electrons travel to the cathode through the external circuit [11].

Despite its promising advantages, solid oxide electrolysis cells (SOECs) have yet to achieve large-scale commercialization and maturity. SOEC technology advancement is challenged by problems such as high manufacturing costs, low stack power, high operating temperature, and short operating life due to thermal stress [5].

Traditional methods, such as laboratory experiments and simulation studies, are already available to support the advancement of SOECs. Experimental studies focus on electrode and catalyst development to improve cell performance and stability, and to lower the cost of input materials used to manufacture SOECs. Jensen et al. [12] fabricated a planar cathode-supported SOEC using LSM-YSZ (anode), YSZ (electrolyte), and Ni-YSZ (cathode) for its components and reported a current density of −3.6 A/cm² and a cell voltage of 1.48 Volts. Liang et al. [13] studied the microstructure and electrochemical performance of SOEC button cells and found that in situ LSM-YSZ composite anodes produced via the glycine–nitrate process (GNP) exhibited better electrolysis performance than traditional LSM and YSZ mixtures. Nechache & Hody [14] reviewed the developments in material optimization for SOEC applications. This study found that yttria-stabilized zirconia (YSZ) is still the reference electrolyte material for cathode-supported cells, while a ScSZ-type material can be the best alternative for electrolyte-supported cells. Moreover, for the H₂ electrode, Ni-YSZ is the most widely used, but alternatives like metal-exsolved perovskites can also be considered. Lastly, for the O₂ electrode, LSM- and LSFC-based materials are widely used, and emerging alternatives like nickelate-based materials could also be explored, given the degradation issues of LSCF and LSM [14].

Simulations, on the other hand, focused on predicting the behavior of SOECs during operation by optimizing operating conditions. Grondin et al. [15] developed a multi-physics model using Butler–Volmer’s law that could estimate the polarization curves of an SOEC, and reported that the temperature distribution depends on gas-feeding configurations. Mendoza et al. [16] developed a 1-D model, combining thermodynamics, kinetic, ohmic, and concentration overpotentials to predict an anode-supported cell’s electrolysis performance. This study found that ohmic loss is a major contributor to the cell’s total overpotential [16]. Menon et al. [17] developed a quasi-two-dimensional model to determine the effect of temperature, H₂/H₂O, and current density on the SOEC performance. This study found that low H₂/H₂O ratios lead to higher current densities but also translate to lower steam utilization rates [17].

Despite the contributions of traditional methods, such as laboratory experiments and numerical and physics-based simulation studies [12,13,14,15,16,17], to the advancement of SOECs, there remains a pressing need for faster, more efficient, and more cost-effective methods to predict SOEC electrochemical performance.

Machine learning has recently gained popularity as the world continues to generate more data. By learning from data directly, ML can transform data into valuable and actionable predictions. Commercial applications of ML include recommendation engines, recognition systems, and image classification [18]. Compared to physical models, which are constrained by explicit governing equations, ML methods can uncover relationships in the data without being explicitly programmed. ML also offers efficient upscaling capability to large systems and datasets without needing extensive computational power. Moreover, once trained, ML models can make accurate predictions in a fraction of a second [19]. However, while machine learning offers a lot of benefits and has many applications in various industries, its limitations should also be acknowledged. Some of the challenges of ML include (1) data size and complexity requirements, (2) extrapolation, (3) interpretability, (4) access issues, and (5) real-world relevance [20].

In recent years, the number of published papers on the application of machine learning in the energy industry has been continuously growing. Allal et al. [21] reviewed ML application to renewable energy sources (RESs) and summarized the four key areas where machine learning can contribute to RESs: (1) fault detection and diagnosis, (2) predictive maintenance, (3) forecasting, (4) resource assessment, (5) optimization, and (6) grid stability analysis. For solid oxide fuel cells (SOFCs), Langner et al. [22] combined the ANN algorithm and simulation to predict the polarization curves of SOFCs and found that the Adam optimizer demonstrated better results in large datasets, while the Levenberg–Marquadt (LM) optimizer performed better in sparse datasets. For other electrolyzer technologies, Shomope et al. [23] studied three machine learning algorithms, Random Forest (RF), Support Vector Machine (SVM), and Extreme Gradient Boosting (XGBoost), to predict hydrogen production in PEM water electrolysis, and found that the Random Forest model consistently outperformed all the other models in predictive performance.

Machine learning has already shown great promise in various energy applications; however, its potential in SOECs remains relatively unexplored. Yang et al. [24] studied multiple machine learning algorithms and found that the improved extreme gradient-enhanced regression (XGBoost) algorithm was the best model for predicting the three target features: ohmic resistance, current, and H₂ production rate. Zhang et al. [25] found that the Extreme Learning Machine (ELM) algorithm is suitable for predicting the current of SOECs using operating voltage and H₂O% as inputs. Fei et al. [26] developed a hybrid ANN model with optimization algorithms to rapidly assess SOEC operating conditions, identifying efficiency improvements through tuning inlet temperature, current density, and excess air ratio.

However, these SOEC–ML studies generally focused on a single output variable, without assessing the ability of ML models to reconstruct polarization (IV) curves across varying operating conditions. Furthermore, these studies have not evaluated how these models perform under interpolation versus extrapolation scenarios.

This study aims to evaluate the feasibility and limitations of using machine learning to predict the shape and behavior of SOEC polarization curves, which are essential in assessing electrochemical performance. To ensure material consistency, this study compiled a dataset of 593 data points from 12 peer-reviewed articles limited to a single cell composition of LSM-YSZ/YSZ/Ni-YSZ. This allowed for focused analysis on operating conditions rather than on material composition variability. Specifically, this study investigated the predictive performance of using the four (4) machine learning algorithms: Support Vector Regressor (SVR), Artificial Neural Network (ANN), Extreme Gradient Boosting (XGBoost), and Random Forest (RF), and evaluate their ability to capture non-linear IV curve behavior under varying operating conditions for both interpolated and extrapolated settings.

The remainder of this paper is organized as follows. Section 2 describes the methodology, including data collection, model development, and evaluation under both interpolation and extrapolation scenarios. Section 3 presents the results alongside a detailed discussion of their implications. Finally, Section 4 summarizes the key findings and outlines the conclusions of this study.

2. Materials and Methods

2.1. Data Collection

Since there is a lack of readily available datasets for model development, data collection and building a dataset from scratch were necessary for this study. Data was collected from published articles on SOEC studies with IV curve results: a total of 12 articles reporting IV curve results for SOECs with LSM-YSZ as the anode, YSZ as the electrolyte, and Ni-YSZ as the cathode. A total of 593 data points were collected from the 12 articles, with a total of 31 IV curves with varying operating conditions and material thickness [12,13,27,28,29,30,31,32,33,34,35,36].

Features collected were categorized into three options: (1) cell characteristics, (2) operating parameters, and (3) electrolytic parameters. Current density and cell voltage values were extracted using the ImageJ software (Version 1.46) from the IV curve plots of the collected journal articles. Using the figure calibration class of the ImageJ software, axis points were carefully calibrated and 10–20 points per curve were gathered, depending on the available data points reported. Other variables describing operating conditions and cell characteristics, such as gas compositions, operating temperature, anode thickness, cathode thickness, electrolyte thickness, and active area, were manually extracted from the published journal articles. The collected data points were stored in Microsoft Excel (Microsoft 365, Version 2507) and saved as a comma-separated file (CSV).

2.2. Data Pre-Processing

The dataset was mounted in Google Colab (Google, CA, USA, https://colab.research.google.com/, accessed on 07 July 2025) and processed using a Jupyter Notebook (Version 6.5.7) for data preparation using the Python (Version 3.12.11) language. The k-nearest neighbors (KNN) imputation method was implemented to handle missing values to ensure that gaps in the dataset were filled based on similar observations. To assess the impact of the KNN imputation, results were compared to the values if the mean imputation method was used. Continuous input features were standardized using scaling methods to prevent bias during model training and reduce the effect of outliers. Feature scaling was performed using a standard scaler method, fitted only to the training data and applied to the test data to avoid data leakage.

2.3. Exploratory Data Analysis

Correlation analysis using the Pearson correlation coefficient or PCC method was conducted to assess pairwise linear relationships between input features. The distribution analysis of the dataset was performed using the box-and-whiskers plot, which is necessary to describe the data collected for the numerical input variables (e.g., operating temperature, current density, component thicknesses, and cell voltage). The correlation heatmap and the box-and-whiskers plots were generated using the Seaborn (Version 0.13.2) and Matplotlib library (Version 3.10.0) in Python.

2.4. Model Development

Data splitting was implemented through a random splitting method to allot 80% of the data for training and 20% for testing for cell voltage predictions. The training dataset was used to train 4 different machine learning algorithms: (1) Random Forest, (2) XGBoost, (3) Artificial Neural Network (ANN), and (4) Support Vector Regression (SVR). Hyperparameter tuning was implemented to obtain the optimal combination of parameters for each model, to achieve the best output variable predictions. The grid search method was used to obtain the best parameters for the models [please see Supplementary Table S2 for the summary of the tuning methods and hyperparameter grid used for each model]. The trained models were then used to predict the test datasets and measure the model’s performance with newly introduced data. The trained and tested models were evaluated using the statistical metrics, coefficient of determination (R²), and Root Mean Squared Error (RMSE) for each machine learning model.

A higher coefficient of determination (R²) suggests a better data fit and indicates a high explanatory power of the model for the output variable. RMSE, on the other hand, quantifies the difference between the predicted and actual values of the model. A smaller RMSE value suggests a smaller discrepancy between the expected and actual values.

2.5. Curve-Based Validation

The generalizability performance of the tuned models was then validated and evaluated using literature data with unseen combinations of operating conditions. Two tests were conducted: (1) Interpolation test and (2) Extrapolation test.

For the interpolation test, four (4) IV curves with 59 data points were isolated and treated as a test dataset. These curves were taken from Jensen et al. [12] with a cathode-supported cell at 850 °C and 50% H₂O, Chen et al. [29] with an anode-supported cell at 700 °C and 50% H₂O, Yang et al. [35] with a cathode-supported cell at 800 °C and 50% H₂O, and, lastly, Sun et al. [36] with a cathode-supported cell at 750 °C and 50% H₂O. Other curves from the mentioned articles were part of the training data set, and the operating conditions are within the bounds of the input space.

For the extrapolation test, two (2) IV curve predictions were made for curves taken from Jensen et al. [12] with a cathode-supported cell at unseen high operating temperature of 950 °C and 70% H₂O, and from Zhu et al. [34] with a cathode-supported cell at unseen and extremely low H₂O% at 2% and 800 °C. These two curves represent operating conditions that are found to be outliers for operating temperature and H₂O%, respectively. To quantify the degree of extrapolation, Mahalanobis distances were computed for each test case using the numerical model input features: anode thickness, electrolyte thickness, cathode thickness, active area, current density (median of IV curve points), temperature, and H₂O%. Distances were then compared with the 95% and 99% thresholds from the training dataset distribution to measure multivariate outlierness. In parallel, univariate percentile ranks were calculated for each of the numerical features to identify which variables exceeded the training data bounds.

The trained and tested models for the interpolation tests and extrapolation tests were evaluated using the statistical metrics, coefficient of determination (R²), and Root Mean Squared Error (RMSE) for each machine learning model used, and predicted IV curves were plotted against the actual IV curves.

2.6. Interpretation

Using the results from the statistical metric evaluations for the test datasets, the four models developed were compared based on statistical metrics and model behavior. The model with the highest R² and smallest RMSE represents the best model for both cell voltage predictions and curve-based validations.

3. Results and Discussion

3.1. Data Profiling

Table 1. Data profiling results of the collected features.

Feature Category	Feature	Range	Unit/s	%Missing
Cell Characteristics	Anode Thickness	10–850	µm	8.43%
	Cathode Thickness	30–500	µm	8.43%
	Electrolyte Thickness	7–1500	µm	8.43%
	Active Area	0.33–63	cm2	0%
Operating Parameters	Temperature	700–950	°C	0%
	Gas Composition (H2O%)	2–99%	%	0%
Electrolytic Parameters	Current Density	−3.611 to −0.002	A/cm2	0%
	Cell Voltage	0.774–1.810	Volts	0%

shows the range of values for each feature collected from the journal articles. Due to the varying cell architecture of the studies collected, the range for the thickness of the electrodes and electrolyte covers a wide range of measurements. It was found that 8.43% of the total dataset was missing for all the thickness features. Some studies do not report the thickness measurements of their tested SOECs. All other features were found to have no missing values.

The features collected are limited to the availability of the reported properties in SOEC studies. Structural characterization properties such as porosity, grain size, interface morphology and other material properties, which could potentially contribute to the accuracy of the IV curve predictions, are currently not consistently being reported in available studies.

KNN imputation was selected to address the missing values because material thickness parameters exhibit strong correlations with other design and operating parameters (e.g., temperature, electrode thickness), which KNN can exploit to produce more realistic estimates. To assess sensitivity to the imputation method, model training was repeated using mean imputation for thickness features. The resulting RMSE changed by <1% for all models, suggesting minimal bias from the imputation choice [please see supplemental Table S2 for the comparison of R and RMSE values]. Although KNN imputation can preserve feature relationships, missing values concentrated in underrepresented SOEC architectures may lead to bias toward the dominant architecture type.

3.2. Exploratory Data Analysis (EDA)

Distribution analysis was carried out to isolate outliers from the numeric variables of the built dataset. Figure 1 shows the distribution of variables, anode thickness, electrolyte thickness, cathode thickness, active area, current density, output voltage, temperature, and H₂O%.

As shown in Figure 1, the anode thickness, cathode thickness, and electrolyte thickness boxplots show the presence of significant outliers. This can be attributed to the cell architecture of the collected articles. Most of the articles are cathode-supported, consistent with the boxplot for cathode thickness with a concentration at around 300–400 µm. The active area is highly right-skewed, with values concentrated in the range of 0.5 cm² to 8 cm². Moreover, the current density boxplot also shows the presence of outliers, and data points are concentrated between −0.2 and −0.8 A/cm², with long-tailed outliers extending below −2 A/cm². One (1) curve from Jensen et al. [12] was tested at 950 °C, and this curve was chosen for the extrapolation IV curve testing. The output variable, cell voltage, ranges from 0.8 V to 1.8 V with a concentration of 1.1–1.4 V. The presence of outliers in the input features was addressed by applying scaling techniques during model development to reduce the effect of outliers on the prediction performance. Operating temperature spans from 700 °C to 950 °C with a concentration around 800 °C to 850 °C. Gas composition (H₂O%) ranges from 2% to 99%, with a concentration of data points around 50%.

The correlation heatmap, Figure 2a, illustrates the relationship between various input features, anode thickness, electrolyte thickness, cathode thickness, active area, current density, temperature, and steam content (H₂O%), and the output variable (output voltage) of solid oxide electrolysis cells (SOECs). From the correlation analysis, there is a strong negative (−0.73) correlation between cathode thickness and anode thickness, indicating that, as cathode thickness increases, anode thickness decreases significantly, and vice versa. This trend may be caused by the cell architecture (e.g., anode-supported vs. cathode-supported), where the thicknesses of the anode and cathode are usually inversely balanced. There is a moderate negative correlation (−0.58) between current density and output voltage, indicating that the output voltage decreases as current density increases. This behavior is consistent with the electrochemical behavior, where increased current density leads to higher ohmic losses and electrode overpotentials, resulting in voltage drops. Moreover, a moderate positive correlation (+0.53) was observed between temperature and cathode thickness. This suggests that, as cathode thickness increases, temperature also increases.

The heat map shown in Figure 2b was generated using the seaborn module on Python to show the distribution of the 31 IV curves collected from 12 articles based on their operating temperatures and gas composition (H₂O%). From the heat map, it can be observed that most of the curves were measured at temperatures of 800 °C and 850 °C and at gas concentrations of 50% and 70% H₂O composition.

3.3. Hyperparameter Tuning

Hyperparameter tuning was performed for each of the models used after training. This was achieved using Python programming via the scikit-learn library. The grid search method was used to produce the best parameters for the models [please see Supplementary Table S2 for the summary of the tuning methods and hyperparameter grid used per model]. A summary of the optimized parameters is shown in

Table 2. Optimized hyperparameters for all the ML algorithms.

Model	Hyperparameters	Optimized Parameters
Random Forest (RF)	N Estimators	200
	Max Depth	16
	Min Samples Split	2
	Min Samples Leaf	2
XGBoost	N Estimators	500
	Max Depth	3
	Learning Rate	0.2
	Subsample	0.8
	Colsample by Tree	1.0
ANN	No. of Hidden Layers	2
	Hidden Layer Size	64
	Activation	ReLU
	Optimizer	Adam (default learning rate = 0.001)
	Epochs	100 (early stopped)
	Batch Size	32
	Early Stopping	Yes, patience = 10
SVR	C	1
	Kernel	Rbf
	Gamma	Scale
	Epsilon	0.01

.

3.4. Cell Voltage Predictions

The performance of four (4) machine learning models, Random Forest (RF), Extreme Gradient Boost (XGBoost), Artificial Neural Network (ANN), and Support Vector Regression (SVR), was evaluated for predicting the output voltage of SOECs. The models were trained on 80% of the dataset and tested on the remaining 20%. Statistical metrics, coefficient of determination (R²), and Root Mean Squared Error (RMSE) were used to evaluate the predictive performance of the models and are summarized in

Table 3. Summary of evaluation metrics for the machine learning models for the cell voltage predictions.

Model	Evaluation Metric	Results
Random Forest (RF)	Training R2	98.41%
	Training RMSE	0.0270
	Testing R2	95.69%
	Testing RMSE	0.0448
XGBoost	Training R2	99.87%
	Training RMSE	0.0077
	Testing R2	98.39%
	Testing RMSE	0.0274
ANN	Training R2	98.70%
	Training RMSE	0.0244
	Testing R2	97.72%
	Testing RMSE	0.0326
SVR	Training R2	93.17%
	Training RMSE	0.0059
	Testing R2	91.02%
	Testing RMSE	0.0647

. The XGBoost model demonstrated the highest performance, with 99.87% R² for training and 98.39% R² for testing. The RF model also achieved high performance, with 98.41% training R² and 95.69% testing R². However, there is a significant drop from training to testing, which indicates a low generalization capability of RF. On the other hand, the ANN model also achieved high performance with 98.70% training R² and 97.72% testing R², and, interestingly, it has the smallest performance gap between training and testing R². This suggests the robust generalization capability of the model, which can capture the underlying relationships without overfitting. Lastly, the SVR model achieved the lowest performance with 93.17% training R² and 91.02% testing R². SVR’s low performance can be attributed to its inability to fully capture non-linear patterns.

3.5. Curve-Based Validation: Interpolation Tests

The performance of the four (4) models was then evaluated using a curve-based validation approach for predicting the IV curves of SOECs via interpolation and extrapolation tests. In the interpolation test, four complete IV curves were isolated as the test dataset to simulate the prediction of unseen combinations of operating conditions that are within the bounds of the input space. The models were also assessed using R² and RMSE and are summarized in

Table 4. Summary of evaluation metrics of the ML models for the curve-based validation for the interpolation scenario.

Model	Evaluation Metric	Results
Random Forest (RF)	Training R2	98.86%
	Training RMSE	0.0223
	Testing R2	98.34%
	Testing RMSE	0.0598
XGBoost	Training R2	99.85%
	Training RMSE	0.0081
	Testing R2	98.10%
	Testing RMSE	0.0332
ANN	Training R2	94.57%
	Training RMSE	0.0488
	Testing R2	92.21%
	Testing RMSE	0.0673
SVR	Training R2	92.85%
	Training RMSE	0.0559
	Testing R2	97.11%
	Testing RMSE	0.0647

.

The Random Forest model achieved high training (98.86%) and testing R² (98.34%) with low RMSE values, indicating the excellent generalizability of the model. The XGBoost model achieved a training R² of 99.85% and testing R² of 98.10% and achieved the lowest RMSE, indicating excellent generalization to unseen data, consistent with the cell voltage prediction results. The ANN model achieved a training R² of 94.57% and testing R² of 92.21%. The relatively low accuracy of ANN could be attributed to its limitations in handling relatively small datasets. Lastly, SVR achieved a training R² of 92.85% and testing R² of 97.11%, suggesting a good generalization to unseen data. Overall, RF and XGBoost emerged as the best-performing models for curve-based validation for the interpolation scenario, with XGBoost having the lowest RMSE.

The resulting individual IV curve predictions of the interpolation tests are illustrated in Figure 3. For Chen et al. [29] and Yang et al. [35], unseen curves at 50% H₂O gas composition were introduced. The model exhibited high predictive performance with an R² value of 98.7% and 97.1%, respectively. This suggests a good generalizability of the model for predictions at 50% H₂O, which is aligned with the findings for the heatmap distribution of the training data, where most of the collected IV curves have gas compositions set at 50%. For Sun et al. [36], an unseen curve at 750 °C was introduced and resulted in a high predictive performance of 97.1%. Although three (3) curves at 850 °C and 50% H₂O were part of the collected data, as shown in Figure 2b, the prediction for Jensen et al. [12] still achieved a lower R² of 93.0% compared to other curves. This may suggest that the curves collected were insufficient to fully represent the variability at this combination of operating conditions, possibly leading to less robust generalization.

3.6. Curve-Based Validation: Extrapolation Test

To test the predictive capability of the XGBoost model at extreme conditions, sample extrapolation tests were also conducted. Two (2) IV curve predictions were made for curves taken from Jensen et al. [12] with a cathode-supported cell at unseen high operating temperature of 950 °C and 70% H₂O, and from Zhu et al. [34] with a cathode-supported cell at unseen and extremely low H₂O% of 2% and operating temperature of 800 °C; these were isolated as test datasets for extrapolated curve-based validations.

Mahalanobis distance analysis (

Table 5. Mahalanobis distance analysis and feature percentile ranks of the extrapolation test cases [12,34].

Test Case	Mahalanobis Distance	95% Threshold	99% Threshold	Multivariate Outlier?	Feature Percentile Ranks 1
1 (Jensen et al. [12])	3.3138	4.3088	5.1154	No	Anode thickness: 0%
					Electrolyte thickness: 12.31%
					Cathode thickness: 36.93%
					Active area: 63.24%
					Current density: 4.05%
					Temperature: 96.12%
					H2O%: 59.70%
2 (Zhu et al. [34])	2.2466	4.3088	5.1154	No	Anode thickness: 39.63%
					Electrolyte thickness: 0%
					Cathode thickness: 80.10%
					Active area: 50.93%
					Current density: 93.42%
					Temperature: 18.38%
					H2O%: 0%

¹ Percentile ranks were calculated relative to the training dataset.

) indicated that neither case exceeded the 95% threshold, suggesting that the overall feature vectors fell within the multivariate distribution of the training dataset. However, the feature percentile ranks revealed that, for test case 1 (Jensen et al. [12] at 950 °C), temperature is part of the top 4% of all training values, while anode thickness and current density were near the minimum observed values. Additionally, for test case 2 (Zhu et al. [34]), H₂O content and electrolyte thickness were at the absolute minimum, and current density is at the top 7% of the of the training values.

Using the XGBoost model, IV curves were plotted in Figure 4a,b. While the XGBoost model IV curve followed a decreasing trend for the cell voltage, it is highly evident that the shape of the predicted curve is far from the literature curve at 950 °C. This finding is also supported by the negative R² of −0.0091%, where a negative R² indicates that the predicted curve is performing worse than just a horizontal line prediction. Similar patterns are also observed with the prediction results at low H₂O% of 2%, having an R² of −369%, which suggests an even poorer prediction performance than that of the outlier temperature test. These results emphasize that, even with low Mahalanobis distances, models can still face risks if some features have extreme values. In such cases, performance drops may be driven by the single extreme values rather than their multivariate profile. The extrapolation findings expose a key limitation of data-driven models such as XGBoost when tested outside the training input distribution: machine learning can approximate relationships based on its learning from historical data, but it does not inherently understand or adapt to the underlying physical principles of material-specific behaviors. SOECs are strongly governed by material-specific properties such as conductivity, porosity, gas diffusivity, and activation energy, which are all highly sensitive to factors such as operating temperature, gas composition, and material configuration. The findings are in agreement with the existing literature that highlights extrapolation as a known weakness of machine learning. Moreover, the findings also emphasize the continued importance of materials science domain knowledge and experimental validation in SOEC advancement.

4. Conclusions

This study demonstrates the viability of machine learning (ML) as a predictive tool for modeling the electrochemical performance of solid oxide electrolysis cells (SOECs) with the material configuration LSM-YSZ/YSZ/Ni-YSZ under trained operating conditions. Four ML models, Support Vector Regressor (SVR), Random Forest (RF), Extreme Gradient Boosting (XGBoost), and Artificial Neural Network (ANN), were evaluated, with XGBoost showing the highest predictive performance. Specifically, XGBoost accurately predicted cell voltage and IV curves across varying gas compositions (50–70% H₂O) and temperatures (700–800 °C), achieving R² values of 98.39% and 98.10%, respectively, within the interpolation range. To explore the limits of model generalization, extrapolation cases were evaluated using Mahalanobis distances and percentile ranking per feature relative to the training dataset distribution. Findings revealed that, even when the overall multivariate distance is below the 95% threshold, certain single features, such as temperature and H₂O%, were far beyond the training range, resulting in poor performance of the IV curve predictions. The findings highlight that, while ML models, like XGBoost, are effective at interpolation, they remain unreliable when faced with untrained, extreme conditions, where they cannot yet fully capture the underlying thermodynamic and microstructural factors influencing SOEC behavior. Moreover, this study emphasizes the critical importance of comprehensive and representative training data. Despite this, the high predictive accuracy within typical operating conditions confirms that machine learning, when applied with appropriate data coverage and guided by materials science concepts, can significantly accelerate SOEC design and optimization.