Physics-Informed Deep Learning for PredictingSuperconducting Critical Temperatures

Abstract

Accurate prediction of superconducting critical temperature (Tc) remains a central challenge in computational materials science. While data-driven machine learning approaches have achieved notable success, they often produce physically inconsistent predictions such as negative transition temperatures. In this work, we propose a Physics-Informed Deep Neural Network (PI-DNN) that incorporates thermodynamic constraints directly into the loss function. Specifically, we enforce non-negativity of Tc (consistent with the Third Law of Thermodynamics) and an upper bound reflecting known physical limits. We benchmark our approach against an XGBoost baseline and a standard DNN of identical architecture on the NIMS superconductivity dataset (21,263 compounds, 81 features). The XGBoost baseline achieves an RMSE of 10.14 K (R2 = 0.911), while the standard DNN yields 11.28 K (R2 = 0.890) and the PI-DNN achieves 10.90 K (R2 = 0.897). The PI-DNN demonstrates a statistically significant improvement over the standard DNN (p < 0.001, paired t-test), while effectively eliminating physically inconsistent predictions. Notably, XGBoost produces 17 negative Tc predictions on the test set, whereas both DNN variants produce zero violations. We discuss the implications of physics-informed constraints as implicit regularizers and their role in building trustworthy materials informatics models