Perovskite oxides (ABO₃) are among the most widely studied cathode materials for SOFCs due to their high electronic and ionic conductivity. ML methods have been extensively applied to accelerate the screening of perovskite compositions with targeted electrochemical properties.

Jacobs et al. developed a ML model based on simple elemental features using random forest (RF) to predict key catalytic properties of perovskites, such as oxygen surface exchange rates, oxygen diffusion rates, and area-specific resistance (ASR)^[42]. The method is shown in Figure 3. The model accurately forecasts ASR with temperature-dependent capabilities and, through temporal validation, demonstrated the ability to identify promising materials like Ba_0.5Sr_0.5Co_0.8Fe_0.2O₃ (BSCF)^[44] years before their experimental discovery. Screening over 19 million compositions revealed several novel, low-cost perovskite candidates containing K, Bi, Y, Ni, and Cu that are predicted to outperform current benchmark materials at reduced temperatures. Zhai et al. proposed a novel method combining the ionic Lewis acid strength (ISA) descriptor with ML to predict efficient ORR electrode materials^[45]. Using an artificial neural network trained on ASR data from 85 perovskite oxides, they screened 6,871 compositions and identified four low-ASR candidates, all experimentally confirmed. Among them, Sr_0.9Cs_0.1Co_0.9Nb_0.1O₃ (SCCN) achieved an ASR of 0.0101 Ω·cm², closely matching prediction. Density functional theory (DFT) revealed that ISA polarization optimizes electronic structure and reduces oxygen vacancy formation and migration barriers^[45].

H-SOFC has gained significant attention in recent years due to its ability to operate at lower temperatures. Numerous studies also have employed AI to screen electrolytes and electrodes for H-SOFC applications. Wang et al. employed a RF model to predict the hydrated proton concentration (HPC) of 3,200 perovskite oxides as a descriptor for evaluating their proton conduction capability^[46]. By analyzing the prediction results, they identified key factors influencing HPC, such as cation radius, tolerance factor, and melting point^[47], and established guidelines for rapidly and accurately designing efficient proton-electron mixed conducting oxides. Based on the prediction results, (La_0.7Ca_0.3)(Co_0.8Ni_0.2)O₃ (LCCN7382) was selected as a potential high-performance air electrode material. Experimental results showed that LCCN7382’s HPC was highly consistent with the predicted value, with current density in electrolysis mode (1,420 mA·cm^-2 at 650 °C) and power density in fuel cell mode (719 mW·cm^-2 at 650 °C)^[46] both superior to most reported protonic ceramic cells (PCCs). Additionally, DFT calculations verified LCCN7382’s high proton conductivity and excellent oxygen reduction/oxygen evolution reaction activity. Subsequently, the team utilized the extreme gradient boosting (XGBoost) algorithm to construct an ML model, predicting the proton absorption amount (PAA) of 27-element-doped Co/Fe-based perovskite oxides^[48]. Through model prediction and DFT calculations, La(Co_0.9Ni_0.1)O₃ (LCN91) was identified as a potential high-performance air electrode material. Experimental results indicated that the proton-conducting solid oxide cells (P-SOC) with LCN91 as the cathode exhibited high current density (843 mA·cm^-2 at 600 °C) in electrolysis mode and high power density (591 mW·cm^-2 at 600 °C) in fuel cell mode^[48]. The study also used DFT calculations to confirm LCN91’s high proton absorption capacity and excellent oxygen reduction/oxygen evolution reaction activity. Tang et al. also employed the XGBoost [Figure 4] algorithm to construct an ML model, predicting the proton absorption capabilities of La_1-xA_xBO₃ (A = Na, K, Ca, Mg, Ba, Cu, etc.) perovskite oxides and identifying La_0.8Ba_0.2CoO₃ (LBC) as a potential high-performance air electrode material^[49]. DFT calculations further confirmed LBC’s high proton absorption capacity. Experimental results showed that the LBC air electrode exhibited high current density (1.72 A·cm^-2 at 600 °C) in electrolysis mode and high power density (1.00 W·cm^-2 at 600 °C) in fuel cell mode, along with an ultra-low air electrode reaction resistance (0.03 Ω·cm² at 600 °C). Additionally, through distributed relaxation time (DRT) analysis and DFT calculations, the researchers explored the water splitting reaction mechanism on the LBC air electrode, identifying the rate-determining step as the dissociation of OH^- intermediates and electron transfer.

In addition to material composition, the microstructure (such as porosity, grain size, and triphase boundary distribution) significantly impacts SOFC performance. Traditional experimental methods are inefficient in optimizing complex microstructures, whereas ML can combine generative models and multiphysics simulations to achieve intelligent design.

Niu et al. proposed a novel deep learning framework called “π learning” [Figure 5] for the microstructural design of high-performance porous electrodes, aiming to generate and optimize electrode microstructures based on electrochemical performance (e.g., the relationship between current density and overpotential)^[50]. The authors combined generative adversarial networks (GANs), convolutional neural networks (CNNs), and multiphysics models to construct the π learning framework. This framework incorporates physical features (such as structural connectivity and active triphase boundary length) during the generation process to guide the creation of microstructures and utilizes experimentally validated multiphysics models to calculate current density as training data labels. The study validated the framework under two strategies: forward design (finding the optimal structure) and inverse design (generating structures with specific performance). Results showed that π learning could successfully generate microstructures close to the target performance and achieve user-specified current density distributions in inverse design. In forward design, combined with the Particle Swarm Optimization algorithm, the framework identified the globally optimal electrode microstructure with the highest current density. Additionally, the study revealed key physical features for optimizing electrodes, such as the impact of porosity and YSZ phase fraction on performance and the importance of the triphase boundary proportion. Peng and Xu employed ML methods to investigate the impact of polycrystalline microstructures on the ionic conductivity of ceramic electrolytes^[51]. They first used the finite element homogenization method to numerically simulate polycrystalline microstructure samples with different grain and grain boundary characteristics, systematically analyzing the effects of grain size, orientation, and grain boundary conductivity on macroscopic ionic conductivity. Based on these findings, they constructed and trained a graph neural network (GNN)-based ML model capable of accurately predicting the effective ionic conductivity of given polycrystalline microstructures. The results indicated that increasing grain size or enhancing grain boundary conductivity could effectively improve ionic conductivity. Moreover, optimizing the distribution of grain orientation and grain boundary conductivity to form conductive pathways further enhanced ionic conductivity.

Stainless steel is the most commonly used material for commercial interconnects in SOFCs due to its low cost and moderate durability. During high-temperature and long-term operation, chromium released from interconnect materials can contaminate the SOFC cathode, severely slowing the ORR and leading to performance degradation, a phenomenon known as chromium poisoning. Yang et al. employed a deep distribution of relaxation times (Deep-DRT) method to evaluate and predict the impact of chromium poisoning and the electrochemical performance degradation of SrFe_0.75M_0.25O_3-δ (SFMO) (M = Co, Fe, Mn, Mo, Nb, Ni) SOFC cathode materials^[52]. The study used symmetric cells with SFMO electrodes fabricated on both sides of a La_0.8Sr_0.2Ga_0.83Mg_0.17O_3-δ (LSGM) electrolyte, conducting chromium poisoning experiments at 700, 750, and 800 °C for 96 h. The measured electrochemical impedance spectroscopy (EIS) data were used as input for training and validating the Deep-DRT model. A set of EIS records for SrFe_0.75Co_0.25O_3-δ (SFCO) at 700 °C for 156 h demonstrated the outstanding accuracy of the MLA method in predicting long-term degradation. Furthermore, the degradation mechanism of SFCO material was analyzed using the predicted DRT, with results consistent with X-ray diffraction (XRD) and scanning electron microscopy (SEM) characterizations. This study showed that the Deep-DRT-based ML method can efficiently and accurately predict the long-term degradation performance and even the degradation mechanisms of SOFC cathode materials.

When using carbon-containing fuels (e.g., natural gas, biogas), Ni-YSZ anodes may experience carbon deposition, known as coking. If the steam-to-carbon ratio falls below a critical value, carbon forms on the Ni catalyst surface, covering active triple-phase boundaries and reducing electrochemical performance^[53]. 3D reconstruction of SOFC electrodes is highly valuable for understanding the relationship between electrochemical performance and microstructural degradation. However, traditional focused ion beam-scanning electron microscopy (FIB-SEM) methods struggle with phase separation. Sciazko et al. proposed a ML-based 3D reconstruction method combining patch-based CNNs^[43]. This approach eliminates the need for resin infiltration of porous samples and enables quantitative microstructural characterization of carbon-deposited Ni-YSZ anodes. The study first observed significant microstructural changes in Ni-YSZ anodes exposed to methane, achieving precise 3D visualization of formed carbon layers and nickel particles. Post-quantitative analysis revealed that under mild conditions, carbon deposition was uniform along the electrode thickness, reducing porosity without completely blocking pores. Instead, it disrupted connections between individual Ni and YSZ grains, causing electrode volume expansion. Under extreme conditions, significant changes in Ni grain size and roughness were observed, with numerous nano-Ni particles found in the carbon layers, indicating metal dusting in high-carbon-activity environments. Mild carbon deposition did not affect active triple-phase boundaries, aligning with performance recovery after carbon removal via humidified hydrogen. Severe coking, however, damaged solid-phase percolation, reducing active reaction sites and causing severe structural and performance degradation. Lyu et al. also used ML to assist in 3D reconstruction and quantitative analysis of carbon deposition in SOFC anodes^[54]. The study employed FIB-SEM to obtain high-resolution images of SOFC anodes after carbon deposition, then used CNNs to segment the images, distinguishing phases such as Ni, YSZ, carbon, and pores, as shown in Figure 6. This process significantly improved segmentation accuracy and efficiency, enabling precise identification of carbon deposition locations and morphologies. Based on the segmented images, 3D reconstruction was performed to analyze the impact of carbon deposition on anode microstructures, including changes in porosity, connectivity, tortuosity, and the microstructures of Ni and YSZ phases. These analyses provided critical microstructural insights into how carbon deposition affects SOFC performance and supported future designs of more carbon-resistant SOFC anodes.

Beyond carbon deposition, SOFC operation can also involve nickel agglomeration and migration^[55,56], nickel oxidation and reduction^[57], ceramic scaffold cracking^[58], phase separation^[59], and poisoning by impurities like sulfur^[60]. Sciazko et al. proposed a ML framework to predict microstructural evolution in SOFC electrodes^[61]. The study used a physics-constrained unsupervised image-to-image translation network (UNIT) to predict nickel oxide reduction processes in Ni-based SOFC anodes. By incorporating physical constraints (e.g., fixed YSZ and GDC skeletons during reduction), the network’s predictive capability was enhanced. Results showed that the UNIT network could predict real-sample microstructural changes with high visual and statistical consistency, even with limited and unpaired training data. Additionally, the conditional UNIT (C-UNIT) network could predict microstructural changes based on reduction temperature and time, providing a powerful tool for studying SOFC electrode microstructural evolution. This method is applicable not only to NiO reduction but also to other degradation-related microstructural changes, such as nickel migration and carbon deposition, offering new perspectives for SOFC performance optimization and lifetime prediction.

Pawłowski et al. used electron tomography and topological data analysis (TDA) to study microstructural evolution in SOFC anodes after long-term operation^[62]. The study employed FIB-SEM to obtain 3D reconstructions of anodes before and after aging, then used persistent homology (PH) to generate persistence diagrams (PDs) quantifying topological feature changes. The study analyzed degradation mechanisms in Ni, pore, and YSZ phases and validated the method’s sensitivity using synthetic microstructures. Results demonstrated that TDA effectively captured microstructural degradation trends, particularly Ni coarsening and pore connectivity changes, offering new insights into SOFC performance degradation. The study also proposed combining PDs with deep learning to further optimize fuel cell performance prediction.

Early fault detection and diagnosis in SOFCs can prevent further damage, extend stack lifespan, reduce unexpected downtime, and improve overall system efficiency.

Zheng et al. proposed a data-driven fault diagnosis method based on principal component analysis (PCA) and support vector machine (SVM) for real-time detection of air leakage and fuel starvation in SOFC systems^[63]. The research team targeted two common fault types in SOFC systems: air leakage and fuel starvation. They collected a large amount of data (approximately 70,000 data sets) from an experimental platform, combined with prior knowledge and statistical feature extraction to develop an online fault diagnosis model. The results showed that this method could effectively identify air leakage and fuel starvation faults in real-time, with an overall classification accuracy of 93.04% and an area under curve (AUC) value as high as 0.997. Compared with traditional ML methods (such as artificial neural networks and RFs), this method exhibited superior performance in prediction accuracy and generalization ability. Le et al. developed a simulation-informed ML algorithm for SOFC system fault diagnosis^[64]. The study used a physical model to simulate EIS responses of an SOFC short stack under normal conditions and three fault modes (uneven fuel distribution, delamination, and oxidant gas leakage), then trained a SVM model with this data. Results showed that different fault modes affected EIS differently: uneven fuel distribution primarily impacted low-frequency gas conversion impedance; delamination increased ohmic and electrode activation impedance; oxidant gas leakage had a smaller but detectable effect on EIS. The SVM model accurately detected and distinguished these faults, demonstrating the potential of EIS as an SOFC fault diagnosis tool. Wu et al. proposed a novel hybrid modeling method for kilowatt-scale SOFC distributed generation systems, using parameters like stack temperature, burner temperature, system efficiency, and current density to assess multi-fault degradation fusion^[65]. The method combined first principles, ML [radial basis function (RBF) neural networks], and multi-modal classification algorithms to build a high-precision dynamic tracking model. The study analyzed the thermal and electrical performance of SOFC stacks and key balance-of-plant components (e.g., burners, heat exchangers, reformers) and validated the model experimentally. Results showed the hybrid model could track system operation trends and identify four typical fault types (heat exchanger rupture, reformer degradation, burner airflow imbalance, and stack degradation), enabling fault severity analysis via multi-modal classification. This provides critical guidance for real-time SOFC system state assessment and efficiency optimization.

In practice, multiple faults often occur simultaneously^[66]. Accurately predicting fault types can optimize control measures, mitigate performance degradation, and enhance SOFC system reliability and durability. Zhang et al. proposed a deep learning-based intelligent simultaneous fault diagnosis method for SOFC systems, addressing air leakage, fuel leakage, and burner exhaust leakage^[67]. The study used stacked sparse autoencoders (SSAEs) for automatic feature extraction and combined them with K-binary classifiers to build a deep neural network (DNN) for diagnosing concurrent fault. Experimental data validated the SSAE model’s effectiveness, outperforming traditional methods (e.g., SVM and PCA-SVM). The method achieved 79.94% accuracy and an F1-score near 90%, demonstrating its potential for real-time SOFC fault monitoring.

Fault prediction in stacks can provide early warnings, prevent performance degradation and safety incidents, and integrate with adaptive control systems for intelligent operation^[68].

Fuel starvation occurs when fuel consumption outpaces supply^[15], leading to nickel oxidation and cell damage^[69]. Ghorbani et al. developed a ML-based virtual hydrogen sensor to detect and quantify the severity of hydrogen starvation in SOFCs^[70]. The study generated nearly 500,000 operational data points using a pseudo-2D numerical model with nine input parameters. Data were randomly split into training and testing sets to evaluate four binary classifiers [K-nearest neighbors (KNN), artificial neural network (ANN), naive Bayes, and logistic regression] and an ANN regression model. Results showed KNN and ANN outperformed others in classification (F1-scores > 0.97), while ANN regression achieved 97.5% accuracy in estimating fuel shortage severity. Experimental validation confirmed the sensor’s effectiveness, offering a new tool for online SOFC monitoring and fault diagnosis.

Ba et al. introduced an ANN-based multi-physics, multi-dimensional model for predicting thermal failure in SOFC stacks^[71]. The study used a unit cell model covering all SOFC physical processes to generate training data for a BP neural network, which replaced complex nonlinear multi-physics equations to rapidly calculate mass and energy source terms in stack model. Comparisons with single-cell tests and 30-layer stack experiments showed high accuracy (~±2% error) and robustness. The model revealed significant temperature distribution differences under various operating conditions, potentially causing thermal stress concentration and failure. It also captured dynamic thermal responses, with electrical, gas composition, and temperature response times of seconds, tens of seconds, and hundreds of seconds, respectively. These findings provide theoretical and practical guidance for real-time thermal failure prediction in SOFC stacks using AI.

Lyu et al. combined long short-term memory (LSTM) networks with dynamic electrochemical impedance spectroscopy (DEIS) to predict SOFC performance degradatio^[72]. The study used over 5,000 h of continuous operation data from an industrial-sized SOFC, including 47 current-voltage (IV) curves and 188 EIS spectra. Preprocessing reduced noise and improved model robustness. The LSTM network trained on historical data predicted future IV curves and EIS spectra with > 0.99 accuracy for short-term (hundreds of hours) predictions, showing strong diagnostic potential. For long-term (thousands of hours) predictions, DEIS analysis quantified degradation mechanisms, identifying their relative importance for durability improvement. The method’s effectiveness in both time and frequency domains could reduce EIS testing time by over 50%, offering robust support for SOFC lifetime prediction.

Wu et al. established data-driven models to predict macro-performance degradation^[73]. Multiple linear regression (MLR) analyzed linear relationships between parameters (operating time, burner temperature, stack temperature, current, load power) and stack voltage. RBF and BP neural networks modeled nonlinear dynamics, with genetic algorithms optimizing BP initial weights and thresholds (GA-BP model). The study also incorporated abnormal shutdown frequency and duration into the model. Results showed the GA-BP model outperformed others, with the lowest mean absolute error (MAE), root mean square error (RMSE), and highest R². Including shutdown factors reduced prediction errors by 68.47%, highlighting significant performance improvements.