Benchmarking empirical and machine-learned interatomic potentials using phase diagram predictions for Lead

TL;DR

This study compares different interatomic potential models for lead, demonstrating that machine-learned potentials can accurately predict phase transitions and outperform traditional models in high-pressure conditions.

Contribution

It introduces a benchmarking framework using nested sampling to evaluate the accuracy of machine-learned potentials versus classical models in phase diagram predictions.

Findings

EDDP captures the FCC-to-HCP transition at ~15 GPa, matching experimental observations.

Traditional EAM and MEAM models predict FCC stability up to 60 GPa, missing the transition.

Nested sampling effectively explores phase stability with modern machine-learned potentials.

Abstract

We compare the predicted phase behaviour of lead (Pb) using three different interatomic potential models, including an embedded atom method (EAM), a modified embedded atom method (MEAM), and a neural network-based machine-learned model in the form of an ephemeral data-derived potential (EDDP). Using nested sampling and replica-exchange nested sampling simulations, we computed thermodynamic and structural properties at pressures up to 60 GPa, mapping both melting behaviour and solid-phase stability. Both the EAM and MEAM models predict the face-centred cubic (FCC) phase to remain stable up to approximately 60 GPa. In contrast, the EDDP model captures the experimentally-observed FCC-to-hexagonal close-packed (HCP) transition at around 15 GPa. These results highlight the importance of training data and model flexibility in accurately describing high-pressure phase behaviour, and demonstrate the effectiveness of nested sampling as a robust framework for exploring phase stability in materials. Particularly, the combination of nested sampling with modern machine-learned interatomic potentials - delivering near ab initio accuracy at tractable cost - opens the door to truly predictive and exhaustive exploration. EDDPs trained on diverse, out-of-equilibrium configurations appear particularly well suited to this task, offering a robust and transferable framework for unbiased phase discovery.