Machine learning (ML), particularly symbolic regression (SR), offers an interpretable approach for discovering quantitative structure-property relationships in materials science. Unlike black-box ML models, SR generates mathematical formulas that can provide direct guidance for materials design. This study focuses on applying SR to accelerate the discovery of new oxide perovskite catalysts, a crucial material family for oxygen evolution reaction (OER) applications in renewable energy technologies. Oxide perovskites (ABO3) are attractive due to their structural flexibility, compositional versatility, and chemical stability. While previous descriptors like reaction free energy and *e_g* occupancy have been used to understand OER activity trends, they often require computationally expensive density functional theory (DFT) calculations. This limits their applicability for designing new materials *a priori*. The study aims to use SR to identify a simpler, more accessible descriptor that can effectively guide the discovery of high-performance oxide perovskite OER catalysts. The researchers synthesized 18 well-studied oxide perovskites to create a consistent dataset for SR analysis. The goal is to identify a descriptor that balances simplicity and accuracy, allowing for efficient screening and discovery of new materials. This descriptor's generality will be validated using independently reported data from other research groups. Finally, new oxide perovskites predicted by the descriptor will be synthesized and characterized to verify the predictions.

The literature review highlights the increasing use of machine learning in materials informatics to accelerate materials design. However, the "black-box" nature of many ML models is criticized for a lack of physical insight, limiting their potential. Symbolic regression (SR) emerges as an interpretable alternative, simultaneously searching for optimal mathematical formulas and parameters. Despite its potential, SR applications in materials science remain limited. The authors discuss existing descriptors for oxide perovskite OER catalysts, including reaction free energy and *e_g* occupancy, but note their limitations due to the dependence on DFT calculations. The need for a simple, physically insightful descriptor that avoids computationally intensive methods is emphasized. A recent review article summarizing the OER activity of oxide perovskites is cited, noting the challenges in comparing data from various sources due to differences in experimental conditions. This highlights the importance of generating a consistent and comparable dataset for the SR analysis.

The methodology involved four main stages: dataset generation, SR analysis, materials design and screening, and experimental verification. Firstly, 18 known oxide perovskite catalysts were synthesized, with each sample undergoing multiple OER measurements under consistent conditions. The resulting *V_RHE* values at five current densities were normalized by catalyst loading and BET surface area, creating a comprehensive dataset. Second, symbolic regression (SR) with genetic programming (GPSR) was employed using the *gplearn* library. Relevant parameters—electronic (number of *d* electrons, electronegativity, valence states) and structural (ionic radii, tolerance factor *t*, octahedral factor *µ*)—were selected based on existing literature. The GPSR algorithm iteratively generated, evaluated, and evolved mathematical formulas (descriptors) based on mean absolute error (MAE) and complexity. A Pareto front analysis was conducted to identify the most accurate and simplest descriptors. Thirdly, the chosen descriptor was used to screen for new oxide perovskites with potentially improved OER activities. Finally, selected candidate materials were synthesized using a modified Pechini method followed by thermal calcination. Their crystal structures were characterized using PXRD, Raman spectroscopy, TEM, STEM, HRTEM, and EDS. OER activity was evaluated using a glassy carbon rotating disk electrode, with potentials referenced to the reversible hydrogen electrode (RHE). Current densities were normalized by loading amount and BET surface area to determine mass and specific activities. The stability of the catalysts was also tested.

Symbolic regression successfully identified the simple descriptor *µ*/t (octahedral factor divided by tolerance factor) as the best predictor of OER activity among numerous candidate descriptors. This descriptor exhibited a linear and monotonic relationship with OER activity, unlike the volcano-shaped relationship observed with conventional descriptors. The *µ*/t descriptor showed strong correlation with experimental data across different studies and time periods, indicating its generality and predictive power. Five new oxide perovskites (Cs_0.25La_0.75Mn_0.5Ni_0.5O₃, Cs_0.4La_0.6Mn_0.25Co_0.75O₃, Cs_0.3La_0.7NiO₃, SrNi_0.75Co_0.25O₃, and Sr_0.25Ba_0.75NiO₃) were synthesized based on predictions from the *µ*/t descriptor. Remarkably, four of these new perovskites demonstrated OER activities comparable to or exceeding those of state-of-the-art oxide perovskite catalysts. The descriptor indicates that lower structural stability (smaller *µ*, larger *t*) correlates with higher OER activity. Further analysis showed that *µ*, *t*, and Q_A (valence state of A-site cation) are more strongly correlated with catalytic activity than other parameters considered. A significant finding was that the highly active oxide perovskites often have a tolerance factor (t) > 1, which is typically considered unstable for perovskites. However, the study demonstrated their synthesizability under suitable conditions.

The study's success in identifying a simple, physically meaningful descriptor for OER activity in oxide perovskites, even with a relatively small dataset, highlights the power of SR in materials discovery. The *µ*/t descriptor offers a practical and computationally inexpensive tool for guiding the design of new catalysts. The linear relationship between *µ*/t and OER activity contrasts with the volcano plots commonly observed for other descriptors, suggesting a different underlying mechanism. The correlation between lower structural stability and higher OER activity is noteworthy and warrants further investigation. The successful synthesis and characterization of four high-performing new perovskites validate the effectiveness of the *µ*/t descriptor in predicting OER activity. The study suggests a new direction in materials discovery by leveraging SR for identifying effective descriptors and guiding the synthesis of high-performance materials.

This research successfully employed symbolic regression to identify a simple yet effective descriptor (*µ*/t) for predicting the oxygen evolution reaction (OER) activity of oxide perovskite catalysts. This descriptor was used to design and synthesize five new perovskites, four of which exhibited superior OER activity compared to existing catalysts. The study demonstrates the potential of symbolic regression in accelerating materials discovery by identifying physically meaningful descriptors and guiding the synthesis of new materials with improved properties. Future research could explore the detailed correlation between *µ*/t, catalytic activity, and structural stability to further refine the descriptor and expand its predictive power.

The study's relatively small dataset (18 known perovskites) for SR training might limit the generalizability of the findings. Further investigation with a larger and more diverse dataset could enhance the robustness and predictive accuracy of the *µ*/t descriptor. The synthesis conditions used might not be optimal for all predicted perovskites, potentially affecting their OER performance. A more comprehensive investigation of synthesis parameters could lead to improved performance in future studies. While four of the five new perovskites synthesized showed improved OER activity, further testing and validation are needed to confirm their long-term stability and performance under various operating conditions.