Discovering new superconductors is challenging, with only a small fraction (around 3%) of candidate materials exhibiting superconductivity. Traditional methods struggle with this low success rate, highlighting the need for innovative approaches. Machine learning (ML), particularly multi-layered feedforward neural networks, offers a promising solution for handling complex datasets and performing classification/regression tasks. Previous attempts to apply ML to superconductivity focused on using random forest methods or convolutional neural networks. However, these approaches often involve discretionary feature selection or rely on inherent patterns within the periodic table, introducing potential biases. This research proposes a novel approach using DeepSets, designed to process unordered sets, providing a more robust and unbiased method.

Prior work using ML for superconductor discovery includes the application of random forest methods to predict Tc (above 10 K) using various chemical characteristics [9]. This method, however, involved subjective choices that could introduce bias. A convolutional neural network approach [11] aimed to bypass this by inputting stoichiometries into a two-dimensional periodic table, treating it as an image. Despite its innovation, this method still depended on the periodic table's inherent structure. DeepSet technology, on the other hand, directly utilizes the chemical composition as an unordered set, avoiding such biases [12].

The proposed method utilizes DeepSet technology, a deep learning algorithm designed to handle unordered sets. The chemical constituents of a compound form the input set. Each element is transformed using a neural network (encoder), and the resulting vectors are summed (pooling operation). The output is then transformed by another neural network (decoder). This avoids artifacts from the order of elements. The method was trained on a dataset of 16395 compounds from the SuperCon database, augmented with data from the Crystallography Open Database (COD) using a "garbage in" approach, where COD materials were labelled as non-superconductors. The SuperCon database was split into training (80%) and test (20%) sets. For classification, a threshold was applied to the output to determine if a material is superconducting. Ensemble techniques were used to improve the results by averaging multiple runs with independent model training, enabling a majority rule for classification. The trained Deep Set was applied to the International Mineralogical Association's mineral list to identify potential superconducting candidates. Three candidates were selected for experimental characterization: synthetic analogues of temagamite (Pd₃HgTe₃), michenerite (PdBiTe), and monchetundraite (Pd₂NiTe₂). Magnetic ac susceptibility was measured to detect superconducting transitions. Additionally, dc magnetization measurements were performed to investigate the critical field of the superconducting phase.

The DeepSet model demonstrated excellent performance in both regression (Tc prediction) and classification (superconductivity identification). The root mean squared error for Tc prediction was 9.5 K (r² = 0.92) for the SuperCon test set and 7 K (r² = 0.84) for the Hosono dataset. Classification results showed high precision and recall, exceeding those reported in previous studies [9, 11]. In the Hosono dataset, with a threshold of 0.85, 29 out of 39 superconductors were correctly identified. Applying the model to the International Mineralogical Association's mineral list identified potential superconducting candidates; 44% of those candidates were already known superconductors. Experimental characterization confirmed superconductivity in synthetic michenerite (PdBiTe) with a Tc of 2.10 K (predicted 1.6 K) and, for the first time, in synthetic monchetundraite (Pd₂NiTe₂) with a Tc of 1.06 K (predicted 1.18 K). Temagamite did not show superconductivity down to 0.45 K. Measurements on three materials predicted to be non-superconducting confirmed their absence of superconducting behavior. Further analysis with a reduced latent space dimension (d=1) allowed for interpretation of individual atomic contributions to superconductivity, providing insights into the significance of certain elements such as Ca.

The DeepSet approach outperforms previous ML methods for superconductor discovery by avoiding biases associated with feature selection and data ordering. The success in predicting Tc and identifying new superconductors demonstrates its potential to accelerate the discovery of novel materials. The ability to trace the contribution of individual atoms provides valuable insights into the underlying mechanisms of superconductivity. The identification of monchetundraite as a superconductor highlights the effectiveness of this AI-driven approach.

This study successfully demonstrates a novel machine learning approach using DeepSet technology to predict the superconductivity and critical temperature of materials. The identification and experimental verification of superconductivity in monchetundraite showcases the method's potential for accelerating the discovery of novel superconductors. Future work should focus on refining the model using larger, higher-quality datasets, including information on synthesis conditions and material properties, to further enhance its predictive power and expand the scope of materials that can be effectively examined.

The study's limitations include the potential influence of impurities in the synthesized samples on the measured critical temperatures and the reliance on available databases, which may not be entirely comprehensive or free from biases. Furthermore, the model's current implementation does not account for factors such as high pressure or thin films, limiting its current predictive power in those domains.