How Can Machine Learning Accelerate CALPHAD Free Energy Modeling?

Abstract

The CALPHAD framework provides a rigorous basis for thermodynamic modeling, yet its ability to predict new chemistries is restricted by limited data and by functional forms that rely heavily on composition alone. Here, we show that machine learning (ML) can address these challenges through a hybrid strategy that learns Redlich-Kister (RK) interaction coefficients directly from physically informed elemental descriptors. Using formation energies of 14-element FCC alloys generated by a universal machine-learning interatomic potential (MLIP), we benchmark three classes of models: (1) composition-based RK and ML models, (2) descriptor-based ML models, and (3) a combined ML-augmented RK approach (ML4RK). Leave-one-element-out tests highlight complementary strengths. RK models, class (1), remain the most data-efficient when binary information is available, while descriptor-based ML models, class (2), enable genuine zero-shot extrapolation to elements absent from the training set. By embedding elemental descriptors into the RK framework, the hybrid approach unifies these regimes and enables prediction of interaction parameters for otherwise unknown or data-scarce binaries, class (3). This work demonstrates a physically grounded and data-efficient route to extend CALPHAD models by combining the transferability of ML with the physical grounding, interpretability, data efficiency, and robustness of thermodynamic formalisms.