Equivariant Evidential Deep Learning for Interatomic Potentials

TL;DR

This paper introduces extit{e}^2IP, an equivariant evidential deep learning framework for interatomic potentials that efficiently quantifies uncertainty in atomic forces during molecular dynamics simulations.

Contribution

It extends evidential deep learning to vector quantities with rotational equivariance, improving uncertainty estimation and data efficiency in interatomic potential modeling.

Findings

extit{e}^2IP outperforms non-equivariant evidential models in accuracy and reliability.

It achieves better data efficiency through equivariant architecture.

extit{e}^2IP maintains single-model inference efficiency while providing uncertainty quantification.

Abstract

Uncertainty quantification (UQ) is critical for assessing the reliability of machine learning interatomic potentials (MLIPs) in molecular dynamics (MD) simulations, identifying extrapolation regimes and enabling uncertainty-aware workflows such as active learning for training dataset construction. Existing UQ approaches for MLIPs are often limited by high computational cost or suboptimal performance. Evidential deep learning (EDL) provides a theoretically grounded single-model alternative that determines both aleatoric and epistemic uncertainty in a single forward pass. However, extending evidential formulations from scalar targets to vector-valued quantities such as atomic forces introduces substantial challenges, particularly in maintaining statistical self-consistency under rotational transformations. To address this, we propose \textit{Equivariant Evidential Deep Learning for Interatomic Potentials} ($\text{e}^2$IP), a backbone-agnostic framework that models atomic forces and their uncertainty jointly by representing uncertainty as a full $3\times3$ symmetric positive definite covariance tensor that transforms equivariantly under rotations. Experiments on diverse molecular benchmarks show that $\text{e}^2$IP provides a stronger accuracy-efficiency-reliability balance than the non-equivariant evidential baseline and the widely used ensemble method. It also achieves better data efficiency through the fully equivariant architecture while retaining single-model inference efficiency.