On the Uncertainty Estimates of Equivariant-Neural-Network-Ensembles Interatomic Potentials

TL;DR

This paper investigates the reliability of uncertainty estimates from equivariant neural network ensembles used as interatomic potentials, revealing that these uncertainties tend to be overconfident and less predictive of actual errors in various configurations.

Contribution

It critically evaluates the robustness of ensemble-based uncertainty estimates for equivariant neural network interatomic potentials applied to silicon, highlighting their limitations in real-world scenarios.

Findings

Uncertainties are generally overconfident.

Ensemble uncertainties have limited quantitative predictive power.

Performance varies across different phases and defect structures.

Abstract

Machine-learning (ML) interatomic potentials (IPs) trained on first-principles datasets are becoming increasingly popular since they promise to treat larger system sizes and longer time scales, compared to the {\em ab initio} techniques producing the training data. Estimating the accuracy of MLIPs and reliably detecting when predictions become inaccurate is key for enabling their unfailing usage. In this paper, we explore this aspect for a specific class of MLIPs, the equivariant-neural-network (ENN) IPs using the ensemble technique for quantifying their prediction uncertainties. We critically examine the robustness of uncertainties when the ENN ensemble IP (ENNE-IP) is applied to the realistic and physically relevant scenario of predicting local-minima structures in the configurational space. The ENNE-IP is trained on data for liquid silicon, created by density-functional theory (DFT) with the generalized gradient approximation (GGA) for the exchange-correlation functional. Then, the ensemble-derived uncertainties are compared with the actual errors (comparing the results of the ENNE-IP with those of the underlying DFT-GGA theory) for various test sets, including liquid silicon at different temperatures and out-of-training-domain data such as solid phases with and without point defects as well as surfaces. Our study reveals that the predicted uncertainties are generally overconfident and hold little quantitative predictive power for the actual errors.