Causal Artificial Intelligence Counterfactual Prediction of Material’s Superconducting Critical Temperature

Ž. Kurtanjek

Abstract
A causal artificial intelligence (AI) model was developed to support the discovery of new superconducting materials by analysing causal relationships between interval-valued elemental descriptors and the superconducting critical temperature, Tc. The aim is to explore a broad elemental composition space without requiring prior knowledge of material structure. Using a University of California, Irvine dataset comprising 21,263 materials with chemical formulae, 81 features, and Tc values were aggregated into temperature-based intervals and analysed within a reproducing kernel Hilbert space framework to infer a causal directed acyclic graph. Three interval features emerged as direct causal drivers of Tc: the standard deviation of mass density, the weighted geometric mean of electron affinity, and the weighted geometric mean of valence. A random forest model using all predictors achieved an R² of approximately 92.9 %, while the causal model, using only these three features, achieved an R² of approximately 89.7 %. Under out-of-distribution splits, the causal model demonstrated superior robustness. Estimated interventional (“do”) effects revealed nonlinear behaviour, and counterfactual analyses of hypothetical interventions further demonstrated the potential of causal AI for guiding exploration of new materials.

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Keywords
superconductivity, causality, counterfactual, Bayes network, reproducing kernel Hilbert space