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Page 16 of 31                       Shu et al. J. Mater. Inf. 2025, 5, 36  https://dx.doi.org/10.20517/jmi.2025.13

               Assessing the stability of optoelectronic materials
               The stability of optoelectronic materials is a critical factor for their long-term performance and durability,
               particularly in applications such as PV devices and catalysis, where material degradation over time can
               significantly affect efficiency and sustainability. Accurately predicting the stability of materials is essential
               for designing durable devices and ensuring their practical viability [131,132] . Recent developments in ML have
               provided powerful tools for predicting the stability of optoelectronic materials [133,134] . This section reviews
               recent advancements in ML-based stability prediction models, highlighting their ability to enhance material
               screening and guide the development of stable, high-performance materials. In recent studies, Bartel et al.
               proposed an improved tolerance factor τ to more accurately predict the stability of perovskite structures,
                                                                               [135]
               addressing the limitations of the traditional Goldschmidt tolerance factor . Based on simple geometric
               relationships, the Goldschmidt factor is somewhat effective for predicting the stability of oxide perovskites,
               but performs inadequately in screening complex materials, especially halide-containing perovskites. To
               overcome these limitations, Bartel and colleagues applied the sure independence screening and sparsifying
               operator (SISSO) method to develop a new one-dimensional descriptor τ, incorporating information about
               ionic radii and oxidation states. This significantly enhances prediction accuracy, achieving a 92% success
               rate for the oxide, fluoride, and chloride perovskites dataset, demonstrating superior performance in
               structural screening compared to the Goldschmidt factor. Figure 7A assesses the performance of τ in
               predicting perovskite stability, illustrating the model accuracy across different chemical combinations and
               its applicability to halide perovskites. Notably, the improved τ factor classifies perovskite stability and
               provides a continuous stability probability estimate P(τ). By applying Platt scaling, Bartel et al. transformed
               the model output into continuous probability values, allowing greater adaptability across various perovskite
                   [135]
               types . Figure 7B shows a stability map for predicted double perovskites, with the lower triangle depicting
               stability probabilities for Cs BB′Cl  compounds and the upper triangle showing La BB′O  compounds. These
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               probability maps, generated from Platt-scaled P(τ) values, use color gradients to indicate the likelihood of
               forming stable perovskite structures across different ion combinations, highlighting potential stability. This
               probability estimate provides researchers with an efficient screening tool for exploring potential perovskite
               materials across broader chemical spaces. Additionally, extensive experimental validation enabled the model
               to predict the stability of 23,314 potential double perovskites, providing a prioritized material list for further
               investigation. This predictive approach lays a solid theoretical foundation for the functional design and
               application of perovskite materials, with significant implications for their development in fields such as PVs
               and electrocatalysis.


               Building on the advancements in stability prediction by Bartel et al., Gu et al. introduced a novel approach
               focused on the synthesizability of perovskite materials based on a graph convolutional neural network
               (GCNN) combined with positive-unlabeled (PU) learning, addressing the limitations of traditional methods
                                                              [136]
               in predicting the practical synthesizability of materials . Traditional stability prediction models, such as
               convex hull energy calculations, primarily assess the thermodynamic stability of materials but are less
               effective at predicting synthesizability under experimental conditions. To overcome this limitation, Gu and
               colleagues pre-trained the GCNN model on actual synthesis data from the MP database and then applied it
               to a perovskite-specific dataset . Using transfer learning, the model achieved significantly improved
                                          [136]
               synthesizability prediction accuracy across different perovskite structures, achieving a true positive rate of
               95.7%. Figure 7C illustrates the model prediction accuracy and data distribution, highlighting the enhanced
               performance of the GCNN and PU learning combination in identifying experimentally synthesized
               materials as positive samples. Furthermore, the model demonstrated its effectiveness in predicting virtual
               perovskites, identifying 179 out of 11,964 virtual perovskite candidates as having potential synthesizability
               based on the model-generated crystal-likeness (CL). Figure 7D compares the GCNN model with screening
               results based on the Goldschmidt rule. The lower left triangle in this figure presents synthesizability scores
               for ABO  perovskite compounds, with a green gradient indicating synthesizability likelihood (deeper green
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