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Machine learning modeling of superconducting critical temperature
Valentin Stanev, Corey Oses, A. Gilad Kusne, Efrain Rodriguez, Johnpierre Paglione, Stefano Curtarolo, Ichiro Takeuchi
TL;DR
The paper addresses the difficult relationship between superconductivity and materials’ chemistry and structure by developing machine-learning models of critical temperature from large superconductor databases. Composition-based classification and family-specific regression perform well, while added crystallographic and electronic features and an integrated screening pipeline extend the approach.
Problem
The relationship between superconductivity and materials’ chemistry and structure remains difficult to understand despite extensive research.
Method
The authors train composition-based random-forest classification and family-specific regression models on SuperCon data, augment predictors with AFLOW information, and combine models to screen ICSD materials.
Results
About 92% out-of-sample accuracy and F1 score are achieved for classifying superconductors above or below 10 K, while decision-level fusion raises recall to about 76%.
Takeaways & Limitations
Large, chemically detailed datasets and complementary predictors support machine-learning analysis of superconducting critical temperatures and candidate-material screening.
Takeaways & Limitations
Training primarily on superconductors risks selection bias, potentially missing effects that inhibit superconductivity in new materials.
Abstract
from arXiv · showhide
Superconductivity has been the focus of enormous research effort since its discovery more than a century ago. Yet, some features of this unique phenomenon remain poorly understood; prime among these is the connection between superconductivity and chemical/structural properties of materials. To bridge the gap, several machine learning schemes are developed herein to model the critical temperatures ($T_{\mathrm{c}}$) of the 12,000+ known superconductors available via the SuperCon database. Materials are first divided into two classes based on their $T_{\mathrm{c}}$ values, above and below 10 K, and a classification model predicting this label is trained. The model uses coarse-grained features based only on the chemical compositions. It shows strong predictive power, with out-of-sample accuracy of about 92%. Separate regression models are developed to predict the values of $T_{\mathrm{c}}$ for cuprate, iron-based, and "low-$T_{\mathrm{c}}$" compounds. These models also demonstrate good performance, with learned predictors offering potential insights into the mechanisms behind superconductivity in different families of materials. To improve the accuracy and interpretability of these models, new features are incorporated using materials data from the AFLOW Online Repositories. Finally, the classification and regression models are combined into a single integrated pipeline and employed to search the entire Inorganic Crystallographic Structure Database (ICSD) for potential new superconductors. We identify more than 30 non-cuprate and non-iron-based oxides as candidate materials.
INTRODUCTION
The paper frames superconductivity as a persistent scientific puzzle, especially the unresolved relationship between materials’ chemistry, structure, and critical temperature. It proposes machine-learning models that exploit expanding materials databases and large-scale composition data to predict Tc and search for new superconductors.
- The mechanisms responsible for high-temperature superconductivity in cuprate and iron-based materials remain elusive despite decades of focused research.
- Machine-learning methods can use extensive measured and calculated materials databases to predict macroscopic properties from collected variables.
- The paper models Tc across reported inorganic superconductors using composition-based predictors, then adds crystallographic and electronic AFLOW features to improve prediction and interpretation.
- More than 16,000 compositions from SuperCon provide subtleties in related compounds, support family-specific modeling, and enhance overall model performance.
- The integrated models screen roughly 110,000 ICSD compositions and highlight 35 compounds with predicted Tc values above 20 K for experimental validation.
RESULTS
Using SuperCon data and random-forest models, the study classifies superconductors around T_c = 10 K, predicts T_c across material families, and identifies composition- and family-specific predictors. The integrated analysis reports strong classification performance, family-dependent regression behavior, and candidate high-T_c materials for further study.
- Dataset: Approximately 16,400 compounds were extracted from SuperCon, including about 5,700 cuprates, 1,500 iron-based materials, and 8,000 other compounds.About 4,000 compounds had no reported T_c.
- Classification: 92% accuracy was achieved for classifying materials above or below T_sep = 10 K, with recall higher than accuracy for the above-threshold class.The above-threshold materials represented approximately 38% of the dataset, and metric values can vary with training and test-set composition.
- Classification: Training-set size and meaningful predictors strongly affect classification, with no obvious saturation at the largest dataset size and almost 90% accuracy using five predictors.Accuracy quickly saturates near 10 predictors; the five were selected from 145 candidates by backward feature elimination.
- Classification: The most important classification predictors include composition-derived variations in column number and electronegativity, elemental melting temperature, and average atomic weight.Materials above 10 K tend to cluster in selected regions of these predictor spaces, including areas with lower mean atomic weights.
- Regression: A general regression model achieved R2 ≈ 0.88 across low-T_c, iron-based, and cuprate superconductors, whereas models trained on one family lacked predictive power for other families.The combined model’s performance is partly a geometric effect because the families occupy mostly distinct T_c ranges.
- Regression: Family-specific predictors indicate distinct superconducting mechanisms, while low atomic weight and low d-electron count are necessary but insufficient conditions for high T_c among low-T_c materials.Predictor relationships also suggest bounds on achievable T_c for non-cuprate/non-iron-based materials and cuprates.
- Regression: The analysis identified a narrow cluster above 20 K involving alkali-doped C60, MgB2-related compounds, and bismuthates, consistent with strong covalent bonding and high-frequency phonons.Bismuthates and chloronitrates also lie above the approximate 1/√m_A trend, suggesting conventional electron-phonon coupling is not driving superconductivity in those materials.
DISCUSSION
The paper develops machine-learning models to study superconducting critical temperatures and connects their predictions to materials chemistry and structure. The integrated models also support screening for candidate high-temperature superconductors.
- DISCUSSION: The study develops classification and regression tools to model superconducting critical temperatures from SuperCon data.The classification separates materials above and below 10 K, while regressors target cuprate, iron-based, and low-Tc groups.
- DISCUSSION: The models use predictor importance to obtain insights into physical mechanisms across different superconducting material groups.
- DISCUSSION: Incorporating AFLOW crystallographic and electronic features further improves the machine-learning models.
- DISCUSSION: Machine-learning models can consume SuperCon and related database records to generate insights into links between materials chemistry, structure, and superconductivity.The authors state that such methods have potential to accelerate searches for candidate high-temperature superconductors.
METHODS
The methods combine SuperCon superconductivity records with AFLOW-derived materials descriptors and random-forest models. Regression errors are analyzed alongside data-quality and database-coverage constraints relevant to prediction and screening.
- Data and predictors: SuperCon supplies experimental critical temperatures and publication records for an exhaustive collection of reported superconductors and related nonsuperconductors.
- Data and predictors: Some SuperCon records have uncertain validity or omit relevant variables such as pressure, limiting the information available to the models.
- Data and predictors: AFLOW contributes reproducible, consistent density-functional-theory-derived crystallographic and electronic features.These include space group, density, volume, energy per atom, electronic entropy, cell valence, dimensional ratios, and Bader-charge statistics.
- Machine learning algorithms: Random-forest algorithms combine predictions from multiple decision trees by voting for classification or averaging for regression.
- Prediction errors of the regression models: Regression models show comparable error spreads that are approximately normally distributed but slightly biased toward underestimating Tc.