Energy Underprediction from Symmetry in Machine-Learning Interatomic Potentials

TL;DR

This paper reveals that current machine learning interatomic potentials systematically underpredict energies, especially in high-symmetry structures, challenging their reliability for materials stability predictions and highlighting the need for symmetry-aware modeling.

Contribution

It identifies symmetry degrees of freedom as a key source of energy underprediction in MLIAPs and suggests incorporating symmetry-aware techniques to improve accuracy.

Findings

Most MLIAPs underpredict energy above hull by over 30 meV/atom.

High-symmetry structures exhibit MAE > 40 meV/atom in energy predictions.

Over 90 ext{ of test structures are in training data, yet errors remain significant}.

Abstract

Machine learning interatomic potentials (MLIAPs) have emerged as powerful tools for accelerating materials simulations with near-density functional theory (DFT) accuracy. However, despite significant advances, we identify a critical yet overlooked issue undermining their reliability: a systematic energy underprediction. This problem becomes starkly evident in large-scale thermodynamic stability assessments. By performing over 12 million calculations using nine MLIAPs for over 150,000 inorganic crystals in the Materials Project, we demonstrate that most frontier models consistently underpredict energy above hull (Ehull), a key metric for thermodynamic stability, total energy, and formation energy, despite the fact that over 90\% of test structures (DFT-relaxed) are in the training data. The mean absolute errors (MAE) for Ehull exceed ~30 meV/atom even by the best model, directly challenging claims of achieving ``DFT accuracy'' for property predictions central to materials discovery, especially related to (meta-)stability. Crucially, we trace this underprediction to insufficient handling of symmetry degrees of freedom (DOF), constituting both lattice symmetry and Wyckoff site symmetries for the space group. MLIAPs exhibit pronounced errors (MAE for Ehull $>$ ~40 meV/atom) in structures with high symmetry DOF, where subtle atomic displacements significantly impact energy landscapes. Further analysis also indicates that the MLIAPs show severe energy underprediction for a large proportion of near-hull materials. We argue for improvements on symmetry-aware models such as explicit DOF encoding or symmetry-regularized loss functions, and more robust MLIAPs for predicting crystal properties where the preservation and breaking of symmetry are pivotal.