# Equivariant Evidential Deep Learning for Interatomic Potentials

arXiv: https://arxiv.org/abs/2602.10419 · HTML: https://mlsanity.com/paper/2602.10419/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 41 references that are in the map.
- First posted on arXiv 11 Feb 2026.

## Builds on (most cited first, 22 of 22)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [Uncertainty Quantification and Deep Ensembles](https://mlsanity.com/paper/2007.08792/) (2020)
- [UMA: A Family of Universal Models for Atoms](https://mlsanity.com/paper/2506.23971/) (2025)
- [Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulations](https://mlsanity.com/paper/2210.07237/) (2022)
- [Deep Ensembles Work, But Are They Necessary?](https://mlsanity.com/paper/2202.06985/) (2022)
- [GemNet-OC: Developing Graph Neural Networks for Large and Diverse Molecular Simulation Datasets](https://mlsanity.com/paper/2204.02782/) (2022)
- [Uncertainty Estimation by Fisher Information-based Evidential Deep Learning](https://mlsanity.com/paper/2303.02045/) (2023)
- [Scaling the leading accuracy of deep equivariant models to biomolecular simulations of realistic size](https://mlsanity.com/paper/2304.10061/) (2023)
- [Single-model uncertainty quantification in neural network potentials does not consistently outperform model ensembles](https://mlsanity.com/paper/2305.01754/) (2023)
- [Lie Algebra Canonicalization: Equivariant Neural Operators under arbitrary Lie Groups](https://mlsanity.com/paper/2410.02698/) (2024)
- [Multivariate Deep Evidential Regression](https://mlsanity.com/paper/2104.06135/) (2021)
- [Uncertainty Estimation for Molecules: Desiderata and Methods](https://mlsanity.com/paper/2306.14916/) (2023)
- [Theoretical Limitations of Ensembles in the Age of Overparameterization](https://mlsanity.com/paper/2410.16201/) (2024)
- [Bayesian E(3)-Equivariant Interatomic Potential with Iterative Restratification of Many-body Message Passing](https://mlsanity.com/paper/2510.03046/) (2025)

## Abstract (arXiv)

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 textitEquivariant Evidential Deep Learning for Interatomic Potentials (e2IP), a backbone-agnostic framework that models atomic forces and their uncertainty jointly by representing uncertainty as a full 3×3 symmetric positive definite covariance tensor that transforms equivariantly under rotations. Experiments on diverse molecular benchmarks show that e2IP 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.