Benchmarking Universal Machine-Learning Interatomic Potentials for Temperature-Dependent Elasticity of Binary and High-Entropy Refractory Carbides

Abstract

Accurate prediction of temperature-dependent elasticity is important for assessing refractory carbides under high-temperature conditions, but the computational cost of ab initio molecular dynamics (AIMD) limits systematic investigations across compositions and temperatures. Universal machine-learning interatomic potentials (uMLIPs) offer an efficient alternative, yet their accuracy for this task remains insufficiently established. Here, we benchmark nine uMLIPs against consistent AIMD reference data for five binary and two high-entropy (HE) carbides between 300 and 1200 K. Elastic constants and the corresponding bulk, shear, and Young's moduli are obtained using stress-strain molecular dynamics, explicitly sampling thermal atomic motion and anharmonic effects beyond thermal expansion alone. We assess absolute elastic properties and normalized thermal softening separately. MACE-MH-1 achieves the lowest overall mean absolute percentage error (5.7%). MACE-MH-1 and DPA4-Mini reproduce thermal softening most accurately, with mean deviations of 2.5 and 2.3 percentage points, respectively. All models generally underestimate stiffness, with larger equilibrium volumes relative to the AIMD reference likely contributing to this trend for most models. C12 exhibits the largest model-dependent errors. The HE carbides are described with accuracy comparable to that of the binary carbides, indicating no apparent accuracy penalty from chemical complexity. Accuracy instead varies with transition-metal composition, with group-V carbides, particularly TaC, presenting the greatest challenge. These results identify promising pretrained models for finite-temperature elasticity in carbides and show why accurate absolute stiffness and thermal softening must be assessed independently.