Learning Smooth and Expressive Interatomic Potentials for Physical Property Prediction

TL;DR

The paper tackles the mismatch between static test-set errors of interatomic potentials and their ability to predict physical properties by emphasizing energy conservation in MD as a practical evaluation. It introduces eSEN, an energy-conserving, equivariant interatomic potential with edgewise and nodewise processing that yields state-of-the-art results across geometry optimization, phonon calculations, thermal conductivity, and materials stability benchmarks. Through targeted design choices—ensuring conservative forces, avoiding discretization-induced artifacts, and maintaining a smoothly varying PES—the authors demonstrate that energy-conserving models exhibit stronger correlations between test errors and downstream property performance. This work suggests that energy-conservation tests can serve as a proxy for rapid development and benchmarking of MLIPs for complex physical-property tasks, accelerating discovery workflows in materials science and chemistry.

Abstract

Machine learning interatomic potentials (MLIPs) have become increasingly effective at approximating quantum mechanical calculations at a fraction of the computational cost. However, lower errors on held out test sets do not always translate to improved results on downstream physical property prediction tasks. In this paper, we propose testing MLIPs on their practical ability to conserve energy during molecular dynamic simulations. If passed, improved correlations are found between test errors and their performance on physical property prediction tasks. We identify choices which may lead to models failing this test, and use these observations to improve upon highly-expressive models. The resulting model, eSEN, provides state-of-the-art results on a range of physical property prediction tasks, including materials stability prediction, thermal conductivity prediction, and phonon calculations.

Figures (14)

• Figure 1: (a) Energy conservation in MD simulations. Direct-force models (Orb, eqV2) and CHGNet fail to conserve. (b) A higher F1 score on the Matbench-Discovery strongly correlates with a lower test-set energy MAE. (c) Test-set energy MAE and $\kappa_{\mathrm{SRME}}$ on the Matbench-Discovery benchmark. (d) Test-set energy MAE and vibrational entropy MAE on the MDR Phonon benchmark. Our model (eSEN) achieves the best performance on all benchmarks. A higher correlation between test-set energy MAE and physical property prediction performance can be observed among energy-conserving models. All models are trained on MPTrj.
• Figure 2: (a) The eSEN architecture. The high-level architecture is similar to Transformer/Equiformer, while the edgewise/nodewise layers are simplified/enhanced. The final-layer $L=0$ features are used to predict nodewise energy, which is summed to get the total potential energy $E$. Forces and stress are obtained through back-propagration. (b) The Edgewise Convolution layer in eSEN.
• Figure 3: Validation loss curves for epoch and wallclock time.
• Figure 4: Conservation error on the TM23 task (top row) and MD22 task (bottom row) for ablating design choices of eSEN. Models that conserve energy are bolded in the legends.
• Figure 5: Predicted phonon band structure and density of states (DOS) of Si (diamond structure), CsCl (CsCl structure), AlN (wurtzite structure) using eSEN at different displacement values. DFT baseline is taken from the PBE MDR dataset loew2024universal calculated using a displacement of 0.01 Å.